Standards Finder

The table on the right shows the abbreviations for the different standards for K-8. For example, if you are a grade 3 teacher looking for Operations and Algebraic Thinking resources, simply input in the field below "NC.3.OA" and you'll see a drop-down list of possible standards for that grade and topic. Then select the appropriate one and press the Apply button.

Range/Course

CC Counting and Cardinality K
OA Operations and Algebraic Reasoning K-5
NBT Numbers and Operations in Base Ten K-5
MD Measurement and Data K-5
G Geometry K-8
NF Numbers and Operations--Fractions 3-5
RP Ratio and Proportional Relationships 6-8
NS The Number System 6-8
EE Expressions and Equations 6-8
SP Statistics and Probability 6-8
F Functions 8
Total Number of Resources: 39736
NC Standards Thumbnail Title Description Curriculum Topic
PC.F.7.2

Definition--Functions and Relations Concepts--Discrete Functions

Definition--Functions and Relations Concepts--Discrete Functions

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Function

Definition--Functions and Relations Concepts--Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Constant Function

Definition--Functions and Relations Concepts--Constant Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Decreasing Function

Definition--Functions and Relations Concepts--Decreasing Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Distorting a Function Vertically

Definition--Functions and Relations Concepts--Distorting a Function Vertically

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Graphs of Functions

Definition--Functions and Relations Concepts--Graphs of Functions

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Graphs of Relations

Definition--Functions and Relations Concepts--Graphs of Relations

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Visualization of the Dependent Variable

Definition--Functions and Relations Concepts--Visualization of the Dependent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Absolute Value Function

Definition--Functions and Relations Concepts--Absolute Value Function

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Function Machine

Definition--Functions and Relations Concepts--Function Machine

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Step Function

Definition--Functions and Relations Concepts--Step Function

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Domain of a Function

Definition--Functions and Relations Concepts--Domain of a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Dependent Variable

Definition--Functions and Relations Concepts--Dependent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Independent Variable

Definition--Functions and Relations Concepts--Independent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Visual Models of Relations

Definition--Functions and Relations Concepts--Visual Models of Relations

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Composite Function

Definition--Functions and Relations Concepts--Composite Function

Quizlet Flash Cards: Composite FunctionsThis is a collection of definitions related to the topic of functions and relations.

Composite Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Vertical Line Test

Definition--Functions and Relations Concepts--Vertical Line Test

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Function Table

Definition--Functions and Relations Concepts--Function Table

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Odd Function

Definition--Functions and Relations Concepts--Odd Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Continuous Function

Definition--Functions and Relations Concepts--Continuous Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Conic Sections

Definition--Functions and Relations Concepts--Conic Sections

This is a collection of definitions related to the topic of functions and relations.

Conic Sections
PC.F.7.2

Definition--Functions and Relations Concepts--Visualization of the Independent Variable

Definition--Functions and Relations Concepts--Visualization of the Independent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Distorting a Function Horizontally

Definition--Functions and Relations Concepts--Distorting a Function Horizontally

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Function Notation

Definition--Functions and Relations Concepts--Function Notation

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Recursive Function

Definition--Functions and Relations Concepts--Recursive Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Range of a Function

Definition--Functions and Relations Concepts--Range of a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Discontinuous Function

Definition--Functions and Relations Concepts--Discontinuous Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Relation

Definition--Functions and Relations Concepts--Relation

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Reflecting a Function

Definition--Functions and Relations Concepts--Reflecting a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Inverse Function

Definition--Functions and Relations Concepts--Inverse Function

This is a collection of definitions related to the topic of functions and relations.

Functions and Their Inverses
PC.F.7.2

Definition--Functions and Relations Concepts--Piecewise Functions

Definition--Functions and Relations Concepts--Piecewise Functions

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Parametric Equations

Definition--Functions and Relations Concepts--Parametric Equations

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Visual Models of Functions

Definition--Functions and Relations Concepts--Visual Models of Functions

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Increasing Function

Definition--Functions and Relations Concepts--Increasing Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Even Function

Definition--Functions and Relations Concepts--Even Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.2

Definition--Functions and Relations Concepts--Translating a Function

Definition--Functions and Relations Concepts--Translating a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Visual Models of Relations

Definition--Functions and Relations Concepts--Visual Models of Relations

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Conic Sections

Definition--Functions and Relations Concepts--Conic Sections

This is a collection of definitions related to the topic of functions and relations.

Conic Sections
PC.F.7.1

Definition--Functions and Relations Concepts--Parametric Equations

Definition--Functions and Relations Concepts--Parametric Equations

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Recursive Function

Definition--Functions and Relations Concepts--Recursive Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Continuous Function

Definition--Functions and Relations Concepts--Continuous Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Discrete Functions

Definition--Functions and Relations Concepts--Discrete Functions

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Function Table

Definition--Functions and Relations Concepts--Function Table

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Absolute Value Function

Definition--Functions and Relations Concepts--Absolute Value Function

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Translating a Function

Definition--Functions and Relations Concepts--Translating a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Vertical Line Test

Definition--Functions and Relations Concepts--Vertical Line Test

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Visualization of the Dependent Variable

Definition--Functions and Relations Concepts--Visualization of the Dependent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Visualization of the Independent Variable

Definition--Functions and Relations Concepts--Visualization of the Independent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Discontinuous Function

Definition--Functions and Relations Concepts--Discontinuous Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Composite Function

Definition--Functions and Relations Concepts--Composite Function

Quizlet Flash Cards: Composite FunctionsThis is a collection of definitions related to the topic of functions and relations.

Composite Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Step Function

Definition--Functions and Relations Concepts--Step Function

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Graphs of Relations

Definition--Functions and Relations Concepts--Graphs of Relations

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Reflecting a Function

Definition--Functions and Relations Concepts--Reflecting a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Function

Definition--Functions and Relations Concepts--Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Function Machine

Definition--Functions and Relations Concepts--Function Machine

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Function Notation

Definition--Functions and Relations Concepts--Function Notation

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Relation

Definition--Functions and Relations Concepts--Relation

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Increasing Function

Definition--Functions and Relations Concepts--Increasing Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Distorting a Function Horizontally

Definition--Functions and Relations Concepts--Distorting a Function Horizontally

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Decreasing Function

Definition--Functions and Relations Concepts--Decreasing Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Visual Models of Functions

Definition--Functions and Relations Concepts--Visual Models of Functions

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Dependent Variable

Definition--Functions and Relations Concepts--Dependent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Constant Function

Definition--Functions and Relations Concepts--Constant Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Odd Function

Definition--Functions and Relations Concepts--Odd Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Independent Variable

Definition--Functions and Relations Concepts--Independent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Distorting a Function Vertically

Definition--Functions and Relations Concepts--Distorting a Function Vertically

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Even Function

Definition--Functions and Relations Concepts--Even Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Range of a Function

Definition--Functions and Relations Concepts--Range of a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Graphs of Functions

Definition--Functions and Relations Concepts--Graphs of Functions

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Inverse Function

Definition--Functions and Relations Concepts--Inverse Function

This is a collection of definitions related to the topic of functions and relations.

Functions and Their Inverses
PC.F.7.1

Definition--Functions and Relations Concepts--Piecewise Functions

Definition--Functions and Relations Concepts--Piecewise Functions

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7.1

Definition--Functions and Relations Concepts--Domain of a Function

Definition--Functions and Relations Concepts--Domain of a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Decreasing Function

Definition--Functions and Relations Concepts--Decreasing Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Continuous Function

Definition--Functions and Relations Concepts--Continuous Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Function Machine

Definition--Functions and Relations Concepts--Function Machine

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Range of a Function

Definition--Functions and Relations Concepts--Range of a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Inverse Function

Definition--Functions and Relations Concepts--Inverse Function

This is a collection of definitions related to the topic of functions and relations.

Functions and Their Inverses
PC.F.7

Definition--Functions and Relations Concepts--Function

Definition--Functions and Relations Concepts--Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Discrete Functions

Definition--Functions and Relations Concepts--Discrete Functions

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7

Definition--Functions and Relations Concepts--Translating a Function

Definition--Functions and Relations Concepts--Translating a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Even Function

Definition--Functions and Relations Concepts--Even Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Visualization of the Independent Variable

Definition--Functions and Relations Concepts--Visualization of the Independent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Absolute Value Function

Definition--Functions and Relations Concepts--Absolute Value Function

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7

Definition--Functions and Relations Concepts--Discontinuous Function

Definition--Functions and Relations Concepts--Discontinuous Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Independent Variable

Definition--Functions and Relations Concepts--Independent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Composite Function

Definition--Functions and Relations Concepts--Composite Function

Quizlet Flash Cards: Composite FunctionsThis is a collection of definitions related to the topic of functions and relations.

Composite Functions
PC.F.7

Definition--Functions and Relations Concepts--Visualization of the Dependent Variable

Definition--Functions and Relations Concepts--Visualization of the Dependent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Recursive Function

Definition--Functions and Relations Concepts--Recursive Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Distorting a Function Horizontally

Definition--Functions and Relations Concepts--Distorting a Function Horizontally

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Increasing Function

Definition--Functions and Relations Concepts--Increasing Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Graphs of Functions

Definition--Functions and Relations Concepts--Graphs of Functions

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Function Table

Definition--Functions and Relations Concepts--Function Table

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Visual Models of Relations

Definition--Functions and Relations Concepts--Visual Models of Relations

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Distorting a Function Vertically

Definition--Functions and Relations Concepts--Distorting a Function Vertically

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Relation

Definition--Functions and Relations Concepts--Relation

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Function Notation

Definition--Functions and Relations Concepts--Function Notation

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Visual Models of Functions

Definition--Functions and Relations Concepts--Visual Models of Functions

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Step Function

Definition--Functions and Relations Concepts--Step Function

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7

Definition--Functions and Relations Concepts--Odd Function

Definition--Functions and Relations Concepts--Odd Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Graphs of Relations

Definition--Functions and Relations Concepts--Graphs of Relations

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Dependent Variable

Definition--Functions and Relations Concepts--Dependent Variable

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Conic Sections

Definition--Functions and Relations Concepts--Conic Sections

This is a collection of definitions related to the topic of functions and relations.

Conic Sections
PC.F.7

Definition--Functions and Relations Concepts--Piecewise Functions

Definition--Functions and Relations Concepts--Piecewise Functions

This is a collection of definitions related to the topic of functions and relations.

Special Functions
PC.F.7

Definition--Functions and Relations Concepts--Vertical Line Test

Definition--Functions and Relations Concepts--Vertical Line Test

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Parametric Equations

Definition--Functions and Relations Concepts--Parametric Equations

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Constant Function

Definition--Functions and Relations Concepts--Constant Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Reflecting a Function

Definition--Functions and Relations Concepts--Reflecting a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.7

Definition--Functions and Relations Concepts--Domain of a Function

Definition--Functions and Relations Concepts--Domain of a Function

This is a collection of definitions related to the topic of functions and relations.

Relations and Functions
PC.F.6.2

Instructional Resource Collection: The Fibonacci Sequence

This is a collection of lessons on the Fibonacci Sequence. There are six lessons. Sequences, Exploring Coordinate Systems, Applications of Exponential and Logarithmic Functions, Ratios and Rates, Proportions, Geometric Constructions with Triangles and Applications of Quadrilaterals
PC.F.6.2

Math Examples Collection: Explicit and Recursive Formulas

This collection aggregates all the math examples around the topic of Explicit and Recursive Formulas. There are a total of 50 Math Examples. This collection of resources is made up of downloadable PNG images that you can easily incorporate into your lesson plans. Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 7

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 7

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 2

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 10

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 10

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 3

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 3

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 9

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 9

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 7

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 7

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 10

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 10

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Instructional Resource--Fibonacci Sequence, Lesson 1

Instructional Resource | Fibonacci Sequence, Lesson 1

The year 2023 is the Year of the Rabbit in the Chinese Zodiac. Media4Math would also like to make this the Year of Fibonacci.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 4

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 4

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Instructional Resource--Fibonacci Sequence, Lesson 5

Instructional Resource | Fibonacci Sequence, Lesson 5

This is a continuation of our exploration of the Fibonacci Sequence. In this lesson we look at the Golden Ratio phi.

Sequences, Ratios and Rates and Proportions
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 8

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 8

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 5

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 5

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 1

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 1

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 5

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 5

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 9

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 9

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 2

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 4

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 4

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 10

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 10

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 8

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 8

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 1

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 1

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 6

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 6

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 6

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 6

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 2

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 9

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 9

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 4

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 4

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 10

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 10

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 7

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 7

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 1

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 1

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 4

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 4

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 6

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 6

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 5

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 5

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 5

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 5

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 9

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 9

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 1

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 1

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 6

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 6

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Instructional Resource--Fibonacci Sequence, Lesson 4

Instructional Resource | Fibonacci Sequence, Lesson 4

This is a continuation of our exploration of the Fibonacci Sequence. In this lesson we look at the Golden Ratio phi.

Sequences, Ratios and Rates and Proportions
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 3

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 3

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Instructional Resource--Fibonacci Sequence, Lesson 6

Instructional Resource | Fibonacci Sequence, Lesson 6

This is a continuation of our exploration of the Fibonacci Sequence. In this lesson we look at geometric constructions that reflect the golden ratio.

Sequences, Geometric Constructions with Triangles and Applications of Quadrilaterals
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 7

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 7

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 3

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 3

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 2

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 5

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 5

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 8

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 8

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 9

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 9

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Instructional Resource--Fibonacci Sequence, Lesson 2

Instructional Resource | Fibonacci Sequence, Lesson 2

This is a continuation of our exploration of the Fibonacci Sequence. In this lesson we look at the sequence as an example of a recursive function.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 2

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 8

Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 8

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 8

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 8

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 7

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 7

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 3

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 3

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 1

Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 1

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 4

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 4

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 10

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 10

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 6

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 6

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 3

Math Example--Sequences and Series--Finding the nth Term of an Arithmetic Sequence: Example 3

This is part of a collection of math examples that focus on sequences and series.

Sequences
PC.F.6.2

Instructional Resource--Fibonacci Sequence, Lesson 3

Instructional Resource | Fibonacci Sequence, Lesson 3

This is a continuation of our exploration of the Fibonacci Sequence. In this lesson we look at the sequence as a logarithmic spiral.

Exploring Coordinate Systems and Applications of Exponential and Logarithmic Functions
PC.F.6.1

Math Video Collection: Texas Instruments Tutorial Videos

This collection aggregates all the math videos and resources in this series: Texas Instruments Tutorial Videos. There are a total of 266 resources. Rational Expressions, Sequences, Series, Polynomial Functions and Equations, Graphs of Quadratic Functions, Quadratic Equations and Functions, Solving Systems of Equations, Trig Expressions and Identities, Probability, Geometric Constructions with Triangles, Composite Functions, Geometric Constructions with Angles and Planes, Distance Formula, Data Analysis, Slope, Special Functions, Trigonometric Functions, Graphs of Exponential and Logarithmic Functions, Radical Functions and Equations, Rational Functions and Equations, Slope-Intercept Form, Coordinate Systems, Graphs of Linear Functions, Inequalities, Matrix Operations and Midpoint Formula
PC.F.6.1

Closed Captioned Video: Exp induction 1

Closed Captioned Video: Exp induction 1

In this TI Nspire tutorial for the TI-Nspire CAS, the Graphing window is used to find the sum of sequence of consecutive integers, as well as deriving the general formu

Sequences and Series
PC.F.6.1

Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Exploring ind

Sequences and Series
PC.F.6.1

Closed Captioned Video: Exp induction 2

Closed Captioned Video: Exp induction 2

In this TI Nspire tutorial for the TI-Nspire CAS, the Graphing window is used to find the sum of sequence of consecutive odd integers, as well as deriving the general f

Sequences and Series
PC.F.6.1

Worksheet: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

Worksheet: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calc

Sequences and Series
PC.F.6.1

Worksheet: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

Worksheet: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

This is part of a collection of math worksheets on the use of the TI-Nspire graphing

Sequences and Series
PC.F.6.1

VIDEO: Ti-Nspire Mini-Tutorial, Video 25

VIDEO: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

In this TI Nspire tutorial for the TI-Nspire CAS, the Graphing window is used to find the sum

Sequences and Series
PC.F.6.1

VIDEO: Ti-Nspire Mini-Tutorial, Video 26

VIDEO: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

In this TI Nspire tutorial for the TI-Nspire CAS, the Graphing window is used to find the

Sequences and Series
PC.F.6.1

Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Exploring inducti

Sequences and Series
PC.F.6

Math Video Collection: Texas Instruments Tutorial Videos

This collection aggregates all the math videos and resources in this series: Texas Instruments Tutorial Videos. There are a total of 266 resources. Rational Expressions, Sequences, Series, Polynomial Functions and Equations, Graphs of Quadratic Functions, Quadratic Equations and Functions, Solving Systems of Equations, Trig Expressions and Identities, Probability, Geometric Constructions with Triangles, Composite Functions, Geometric Constructions with Angles and Planes, Distance Formula, Data Analysis, Slope, Special Functions, Trigonometric Functions, Graphs of Exponential and Logarithmic Functions, Radical Functions and Equations, Rational Functions and Equations, Slope-Intercept Form, Coordinate Systems, Graphs of Linear Functions, Inequalities, Matrix Operations and Midpoint Formula
PC.F.6

Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Exploring ind

Sequences and Series
PC.F.6

VIDEO: Ti-Nspire Mini-Tutorial, Video 25

VIDEO: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

In this TI Nspire tutorial for the TI-Nspire CAS, the Graphing window is used to find the sum

Sequences and Series
PC.F.6

Closed Captioned Video: Exp induction 1

Closed Captioned Video: Exp induction 1

In this TI Nspire tutorial for the TI-Nspire CAS, the Graphing window is used to find the sum of sequence of consecutive integers, as well as deriving the general formu

Sequences and Series
PC.F.6

Worksheet: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

Worksheet: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calc

Sequences and Series
PC.F.6

Closed Captioned Video: Exp induction 2

Closed Captioned Video: Exp induction 2

In this TI Nspire tutorial for the TI-Nspire CAS, the Graphing window is used to find the sum of sequence of consecutive odd integers, as well as deriving the general f

Sequences and Series
PC.F.6

Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Integers

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Exploring inducti

Sequences and Series
PC.F.6

Worksheet: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

Worksheet: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

This is part of a collection of math worksheets on the use of the TI-Nspire graphing

Sequences and Series
PC.F.6

VIDEO: Ti-Nspire Mini-Tutorial, Video 26

VIDEO: TI-Nspire Mini-Tutorial: (CAS) Exploring induction: Finding the Formula for the Sum of Consecutive Odd Integers

In this TI Nspire tutorial for the TI-Nspire CAS, the Graphing window is used to find the

Sequences and Series
PC.F.5.7

Math Definitions Collection--Calculus Concepts

This collection aggregates all the definitions for key terms in a standards Calculus course. There are a total of 88 images. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation. Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Power Rule

Definition--Calculus Topics--Power Rule

The process of finding the derivative of a power function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Linear Approximation

Definition--Calculus Topics--Linear Approximation

For differentiable function f(x), the linear approximation at x = a, for some real number a, is the equation of the line tangent to f(x) at a.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Zeros of a Function

Definition--Calculus Topics--Zeros of a Function

Where the graph of a function intersects the x-axis. The solutions to the equation f(x) = 0 for some function f(x).

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Change of Variables

Definition--Calculus Topics--Change of Variables

A substitution technique where a variable replaces a more complicated expression. In calculus it can simplify differentiation or integration.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Differential Equation

Definition--Calculus Topics--Differential Equation

An equation that includes the derivative of a function f(x) and the variable x.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Rational Function

Definition--Calculus Topics--Rational Function

A function made up of the ratio of two functions f(x) and g(x).

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Derivative

Definition--Calculus Topics--Derivative

A function used to find the slope of a tangent to a curve at a given point. The derivative is based on the following limit.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Acceleration

Definition--Calculus Topics--Acceleration

The second derivative, with respect to time, for the displacement function. Acceleration is a vector quantity.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Instantaneous Rate of Change

Definition--Calculus Topics--Instantaneous Rate of Change

Another way of describing the slope of the line tangent to a given curve at a given point.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Mean Value Theorem

Definition--Calculus Topics--Mean Value Theorem

For differentiable function f(x) along the closed interval [a, b] there is a value c within that interval such that f'(c) is parallel to the secant formed by th

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Absolute Value Function

Definition--Calculus Topics--Absolute Value Function

A piecewise function whose simplest form is shown below. These functions are not differentiable at their vertex.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--End Behavior

Definition--Calculus Topics--End Behavior

The way a function f(x) changes as x approaches infinity, whether positive or negative.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Chain Rule

Definition--Calculus Topics--Chain Rule

The process for finding the derivative of a composite function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Derivative of an Exponential Function

Definition--Calculus Topics--Derivative of an Exponential Function

The derivative of an exponential function is the product of the function and the natural log of the base. The derivative of ex is ex.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Discontinuous Function

Definition--Calculus Topics--Discontinuous Function

A function is discontinuous if it has one or more gaps along the domain of the function. The left- or right-hand limits exist but are not equal.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Derivative of a Composite Function

Definition--Calculus Topics--Derivative of a Composite Function

For two functions f(x) and g(x), the derivative of the composite function f(g(x)) is f'(x)*g'(x). This is an example of the Chain Rule.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Inverse Function

Definition--Calculus Topics--Inverse Function

For function f(x), the inverse function f-1(x), if it exists, undoes the mapping of the original function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Velocity

Definition--Calculus Topics--Velocity

The first derivative, with respect to time, for the displacement function. Velocity is a vector quantity.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Definite Integral

Definition--Calculus Topics--Definite Integral

The integral of a function with specific limits on the endpoints. A definite integral results in a numerical value.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Parametric Equations

Definition--Calculus Topics--Parametric Equations

A set of equations where each variable, x and y, is a function of a third variable, t. Graphs of parametric equations are sometimes not functions.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Delta y

Definition--Calculus Topics--Delta y

The change in y-coordinates for a given function. Often used in the formula for finding the derivative of a function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Derivative of a Rational Function

Definition--Calculus Topics--Derivative of a Rational Function

Since a rational function is the ratio of two polynomials, the derivative of a rational function is also the ratio of two polynomials.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Discrete Function

Definition--Calculus Topics--Discrete Function

A function whose graphs has gaps. This is because the function consists of separate ordered pairs or is a discontinuous function with gaps.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Sum Rule

Definition--Calculus Topics--Sum Rule

For differentiable functions f(x) and g(x) along a given interval, the derivative of the sum f(x) + g(x) is the sum of the individual derivatives f'(x) and g'(x).

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Tangent to a Curve

Definition--Calculus Topics--Tangent to a Curve

A line that intersects a curve at a single point and is perpendicular to the curve at that point.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Step Function

Definition--Calculus Topics--Step Function

A discontinuous function whose graph looks like a staircase. A step function can be generated by ceiling or floor functions.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Integration by Substitution

Definition--Calculus Topics--Integration by Substitution

Replacing the integrand with a simpler expression to make the process of integration easier.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Continuous Functions

Definition--Calculus Topics--Continuous Functions

A function is continuous if it has no gaps along the domain of the function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Extreme Value Theorem

Definition--Calculus Topics--Extreme Value Theorem

For function f(x) along an interval, there are maximum and minimum values. If the derivative is zero along this interval, this is an inflection point.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Oblique Asymptote

Definition--Calculus Topics--Oblique Asymptote

A slanted line that the graph of a function approaches but does not intersect.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Hooke's Law

Definition--Calculus Topics--Hooke's Law

A second-order differential equation that is used to model simple harmonic motion using a trigonometric function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Rolle's Theorem

Definition--Calculus Topics--Rolle's Theorem

For function f(x) along an interval [a, b], if f(a) = f(b), then there is a point along the interval where the derivative is zero.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Implicit Differentiation

Definition--Calculus Topics--Implicit Differentiation

When a function cannot be written in the form of y as a function of x, then implicit differentation can be used to find the derivative with respect to x.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Trigonometric Function

Definition--Calculus Topics--Trigonometric Function

One of six main functions, including sine, cosine, tangent, secant, cosecant, and cotangent.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Left-Hand Limit

Definition--Calculus Topics--Left-Hand Limit

As a function f(x) approaches a specific input value a, for x-values less than or equal to a, the function may approach a specific limiting value.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Indefinite Integral

Definition--Calculus Topics--Indefinite Integral

The integral of a function without a specific limit on the endpoints. The result of an indefinite integral is a differentiable function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Integral

Definition--Calculus Topics--Integral

A method for finding the area of a curve along an interval. In calculus, integrating a function f(x) involves finding the antiderivative of f(x).

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Absolute Minimum

Definition--Calculus Topics--Absolute Minimum

When a function takes an input value, a, for some value in the domain, such that f(a) ≤ f(x), for all x in the domain.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Vector

Definition--Calculus Topics--Vector

A quantity that has magnitude and direction. Vectors are often used to model real-world phenomena such as force, speed, or acceleration.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Even Function

Definition--Calculus Topics--Even Function

A function whose graph is symmetric about the y-axis.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Right-Hand Limit

Definition--Calculus Topics--Right-Hand Limit

As a function f(x) approaches a specific input value a, for x-values greater than or equal to a, the function may approach a specific limiting value.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Sigma Notation

Definition--Calculus Topics--Sigma Notation

The Greek letter used for summarizing terms of a finite or infinite sequence.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Trig Identities

Definition--Calculus Topics--Trig Identities

Equations that involve trigonmetric functions and are often used to simplify certain trigonometric expressions.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Derivative of a Quadratic Function

Definition--Calculus Topics--Derivative of a Quadratic Function

Since a quadratic function is a polynomial function of degree 2, the derivative is a linear function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Derivative of a Logarithmic Function

Definition--Calculus Topics--Derivative of a Logarithmic Function

The derivative of a logarithmic function uses the laws of logarithms and the definition of e to find the derivative.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Delta x

Definition--Calculus Topics--Delta x

The change in x-coordinates for a given function. Often used in the formula for finding the derivative of a function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Matrix Representations of Vectors

Definition--Calculus Topics--Matrix Representations of Vectors

A vector quantity can be represented by a matrix.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Integrand

Definition--Calculus Topics--Integrand

In the process of integration, it is the function that is being integrated.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Limits at Infinity

Definition--Calculus Topics--Limits at Infinity

Finding the limiting value for function f(x) as the input value x approaches infinity. This limit may or may not exist.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Explicit Function

Definition--Calculus Topics--Explicit Function

A function in which y can be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equation.

Calculus Vocabulary
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Definition--Calculus Topics--Piecewise Function

Definition--Calculus Topics--Piecewise Function

A function made up of separate functions, each with its own interval.

Calculus Vocabulary
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Definition--Calculus Topics--Asymptote

Definition--Calculus Topics--Asymptote

A line that the graph of a function approaches but does not intersect. Asymptotes can be vertical, horizontal, or oblique.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Power Function

Definition--Calculus Topics--Power Function

A function with a single term that consists of a variable base raised to a real number power. The variable can also have a real number coefficient.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Derivative of a Linear Function

Definition--Calculus Topics--Derivative of a Linear Function

The derivative of a linear function of the form y = mx + b is the slope of the line, m.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Horizontal Asymptote

Definition--Calculus Topics--Horizontal Asymptote

A horizontal line that the graph of a function approaches but does not intersect. The equation of a horizontal asymptote is y = c, for some constant c.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Antiderivative

Definition--Calculus Topics--Antiderivative

For two differentiable functions f(x) and F(x), if F'(x) = f(x), then F(x) is the antiderivative of f(x).

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Quotient Rule

Definition--Calculus Topics--Quotient Rule

The rule for finding the derivative of a function made up of the ratios of two functions f(x) and g(x).

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Floor Function

Definition--Calculus Topics--Floor Function

A discrete function that takes real number values and whose output is the greatest integer value greater than the input value. The graph looks like a staircase.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Separable Differential Equation

Definition--Calculus Topics--Separable Differential Equation

A special type of differential equation in which functions f(x) and g(y) can be separated to find the solution to the equation.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Concave Function

Definition--Calculus Topics--Concave Function

A function whose graph curves down along an interval of the domain. The inflection point is where the first derivative is zero.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Intermediate Value Theorem

Definition--Calculus Topics--Intermediate Value Theorem

For continuous function f(x) along interval [a, b] there are values between f(a) and f(b).

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--One-Sided Limits

Definition--Calculus Topics--One-Sided Limits

Restricting the limit of a function for values approaching the limiting value from one side.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Derivative of a Polynomial Function

Definition--Calculus Topics--Derivative of a Polynomial Function

The derivative of a polynomial of degree n is another polynomial of degree n - 1.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Inflection Point

Definition--Calculus Topics--Inflection Point

The point on a curve where the curvature changes. This is often indicated by a change in the slopes of tangents to the curve.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Ceiling Function

Definition--Calculus Topics--Ceiling Function

A discrete function that takes real number values and whose output is the least integer value greater than the input value. The graph looks like a staircase.

Calculus Vocabulary
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Definition--Calculus Topics--Derivative of a Trig Function

Definition--Calculus Topics--Derivative of a Trig Function

The derivative of a trig function is another trig function, as shown in the table.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Use implicit differentiation and the quotient rule to find the derivative of an inverse trig function.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Absolute Maximum

Definition--Calculus Topics--Absolute Maximum

When a function takes an input value, a, for some value in the domain, such that f(a) ≥ f(x), for all x in the domain.

Calculus Vocabulary
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Definition--Calculus Topics--Differentiation

Definition--Calculus Topics--Differentiation

The process of finding the derivative of a function.

Calculus Vocabulary
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Definition--Calculus Topics--Average Rates of Change

Definition--Calculus Topics--Average Rates of Change

The ratio along an interval of a domain for a given function, comparable to calculating the slope of a line.

Calculus Vocabulary
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Definition--Calculus Topics--Displacement Function

Definition--Calculus Topics--Displacement Function

A distance-vs.-time function used to find the distance an object has moved from a starting point.

Calculus Vocabulary
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Definition--Calculus Topics--Area Beneath a Curve

Definition--Calculus Topics--Area Beneath a Curve

For a definite integral, it is the numerical result of the integration.

Calculus Vocabulary
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Definition--Calculus Topics--Local Maximum

Definition--Calculus Topics--Local Maximum

When a function takes an input value, a, for some region in the domain, such that f(a) ≥ f(x), for all x in that region.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Fundamental Theorem of Calculus

Definition--Calculus Topics--Fundamental Theorem of Calculus

The theorem that relates differentiation and integration. The two operations are basically inverses of each other.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Convex Function

Definition--Calculus Topics--Convex Function

A function whose graph curves up along an interval of the domain. The inflection point is where the first derivative is zero.

Calculus Vocabulary
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Definition--Calculus Topics--Odd Function

Definition--Calculus Topics--Odd Function

A function whose graph has point symmetry about the origin.

Calculus Vocabulary
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Definition--Calculus Topics--Trapezoidal Rule

Definition--Calculus Topics--Trapezoidal Rule

A technique for approximating a definite integral by adding the areas of trapezoids underneath a curve.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Composite Function

Definition--Calculus Topics--Composite Function

A function whose input values are made up of another function. For two functions f(x) and g(x), a composite function can be written as f(g(x)).

Calculus Vocabulary
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Definition--Calculus Topics--Integral Symbol

Definition--Calculus Topics--Integral Symbol

The mathematical symbol used to denote the process of integration.

Calculus Vocabulary
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Definition--Calculus Topics--Riemann Sum

Definition--Calculus Topics--Riemann Sum

An approximation method for estimating the area under a curve and used to approximate the solution to a definite integral.

Calculus Vocabulary
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Definition--Calculus Topics--Implicit Function

Definition--Calculus Topics--Implicit Function

A function in which y cannot be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equatio

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--L'Hopital's Rule

Definition--Calculus Topics--L'Hopital's Rule

For function f(x)/g(x), where f(x) and g(x) are two functions, along an interval [a, b], if there is a point c in the interval such that g(x) = 0, then L'Hopital'

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Second Derivative

Definition--Calculus Topics--Second Derivative

For differentiable function f(x), the second derivative is the derivative of f'(x) and denoted as f''(x).

Calculus Vocabulary
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Definition--Calculus Topics--Differentiable Function

Definition--Calculus Topics--Differentiable Function

A function is differentiable if a derivative can be found at each point in its domain.

Calculus Vocabulary
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Definition--Calculus Topics--Vertical Asymptote

Definition--Calculus Topics--Vertical Asymptote

A vertical line that the graph of a function approaches but does not intersect. The equation of a vertical asymptote is x = c, for some constant c.

Calculus Vocabulary
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Definition--Calculus Topics--First Derivative

Definition--Calculus Topics--First Derivative

For differentiable function f(x), the first derivative is denoted as f'(x).

Calculus Vocabulary
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Definition--Calculus Topics--Local Minimum

Definition--Calculus Topics--Local Minimum

When a function takes an input value, a, for some region in the domain, such that f(a) ≤ f(x), for all x in that region.

Calculus Vocabulary
PC.F.5.7

Definition--Calculus Topics--Limit

Definition--Calculus Topics--Limit

As a function f(x) approaches a specific input value a, the function may approach a specific limiting value. This limit may or may not exist.

Calculus Vocabulary
PC.F.5.6

INSTRUCTIONAL RESOURCE: Math Examples 18

INSTRUCTIONAL RESOURCE: Math Examples--Functions and Their Inverses

This set of tutorials provides 18 examples that explore the concept of functions and their inverses.

Functions and Their Inverses
PC.F.5.5

Math Definitions Collection--Calculus Concepts

This collection aggregates all the definitions for key terms in a standards Calculus course. There are a total of 88 images. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation. Calculus Vocabulary
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Definition--Calculus Topics--Implicit Differentiation

Definition--Calculus Topics--Implicit Differentiation

When a function cannot be written in the form of y as a function of x, then implicit differentation can be used to find the derivative with respect to x.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Matrix Representations of Vectors

Definition--Calculus Topics--Matrix Representations of Vectors

A vector quantity can be represented by a matrix.

Calculus Vocabulary
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Definition--Calculus Topics--Tangent to a Curve

Definition--Calculus Topics--Tangent to a Curve

A line that intersects a curve at a single point and is perpendicular to the curve at that point.

Calculus Vocabulary
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Definition--Calculus Topics--Integrand

Definition--Calculus Topics--Integrand

In the process of integration, it is the function that is being integrated.

Calculus Vocabulary
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Definition--Calculus Topics--Discontinuous Function

Definition--Calculus Topics--Discontinuous Function

A function is discontinuous if it has one or more gaps along the domain of the function. The left- or right-hand limits exist but are not equal.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Mean Value Theorem

Definition--Calculus Topics--Mean Value Theorem

For differentiable function f(x) along the closed interval [a, b] there is a value c within that interval such that f'(c) is parallel to the secant formed by th

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Limit

Definition--Calculus Topics--Limit

As a function f(x) approaches a specific input value a, the function may approach a specific limiting value. This limit may or may not exist.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Absolute Maximum

Definition--Calculus Topics--Absolute Maximum

When a function takes an input value, a, for some value in the domain, such that f(a) ≥ f(x), for all x in the domain.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Sum Rule

Definition--Calculus Topics--Sum Rule

For differentiable functions f(x) and g(x) along a given interval, the derivative of the sum f(x) + g(x) is the sum of the individual derivatives f'(x) and g'(x).

Calculus Vocabulary
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Definition--Calculus Topics--Horizontal Asymptote

Definition--Calculus Topics--Horizontal Asymptote

A horizontal line that the graph of a function approaches but does not intersect. The equation of a horizontal asymptote is y = c, for some constant c.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Trigonometric Function

Definition--Calculus Topics--Trigonometric Function

One of six main functions, including sine, cosine, tangent, secant, cosecant, and cotangent.

Calculus Vocabulary
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Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Use implicit differentiation and the quotient rule to find the derivative of an inverse trig function.

Calculus Vocabulary
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Definition--Calculus Topics--Absolute Value Function

Definition--Calculus Topics--Absolute Value Function

A piecewise function whose simplest form is shown below. These functions are not differentiable at their vertex.

Calculus Vocabulary
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Definition--Calculus Topics--Trapezoidal Rule

Definition--Calculus Topics--Trapezoidal Rule

A technique for approximating a definite integral by adding the areas of trapezoids underneath a curve.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Average Rates of Change

Definition--Calculus Topics--Average Rates of Change

The ratio along an interval of a domain for a given function, comparable to calculating the slope of a line.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Asymptote

Definition--Calculus Topics--Asymptote

A line that the graph of a function approaches but does not intersect. Asymptotes can be vertical, horizontal, or oblique.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Delta y

Definition--Calculus Topics--Delta y

The change in y-coordinates for a given function. Often used in the formula for finding the derivative of a function.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Linear Approximation

Definition--Calculus Topics--Linear Approximation

For differentiable function f(x), the linear approximation at x = a, for some real number a, is the equation of the line tangent to f(x) at a.

Calculus Vocabulary
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Definition--Calculus Topics--Rational Function

Definition--Calculus Topics--Rational Function

A function made up of the ratio of two functions f(x) and g(x).

Calculus Vocabulary
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Definition--Calculus Topics--Area Beneath a Curve

Definition--Calculus Topics--Area Beneath a Curve

For a definite integral, it is the numerical result of the integration.

Calculus Vocabulary
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Definition--Calculus Topics--Inflection Point

Definition--Calculus Topics--Inflection Point

The point on a curve where the curvature changes. This is often indicated by a change in the slopes of tangents to the curve.

Calculus Vocabulary
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Definition--Calculus Topics--Even Function

Definition--Calculus Topics--Even Function

A function whose graph is symmetric about the y-axis.

Calculus Vocabulary
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Definition--Calculus Topics--Concave Function

Definition--Calculus Topics--Concave Function

A function whose graph curves down along an interval of the domain. The inflection point is where the first derivative is zero.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Riemann Sum

Definition--Calculus Topics--Riemann Sum

An approximation method for estimating the area under a curve and used to approximate the solution to a definite integral.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Local Maximum

Definition--Calculus Topics--Local Maximum

When a function takes an input value, a, for some region in the domain, such that f(a) ≥ f(x), for all x in that region.

Calculus Vocabulary
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Definition--Calculus Topics--Step Function

Definition--Calculus Topics--Step Function

A discontinuous function whose graph looks like a staircase. A step function can be generated by ceiling or floor functions.

Calculus Vocabulary
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Definition--Calculus Topics--Antiderivative

Definition--Calculus Topics--Antiderivative

For two differentiable functions f(x) and F(x), if F'(x) = f(x), then F(x) is the antiderivative of f(x).

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Implicit Function

Definition--Calculus Topics--Implicit Function

A function in which y cannot be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equatio

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Hooke's Law

Definition--Calculus Topics--Hooke's Law

A second-order differential equation that is used to model simple harmonic motion using a trigonometric function.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Delta x

Definition--Calculus Topics--Delta x

The change in x-coordinates for a given function. Often used in the formula for finding the derivative of a function.

Calculus Vocabulary
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Definition--Calculus Topics--Differentiation

Definition--Calculus Topics--Differentiation

The process of finding the derivative of a function.

Calculus Vocabulary
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Definition--Calculus Topics--Right-Hand Limit

Definition--Calculus Topics--Right-Hand Limit

As a function f(x) approaches a specific input value a, for x-values greater than or equal to a, the function may approach a specific limiting value.

Calculus Vocabulary
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Definition--Calculus Topics--Derivative of a Logarithmic Function

Definition--Calculus Topics--Derivative of a Logarithmic Function

The derivative of a logarithmic function uses the laws of logarithms and the definition of e to find the derivative.

Calculus Vocabulary
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Definition--Calculus Topics--Differential Equation

Definition--Calculus Topics--Differential Equation

An equation that includes the derivative of a function f(x) and the variable x.

Calculus Vocabulary
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Definition--Calculus Topics--End Behavior

Definition--Calculus Topics--End Behavior

The way a function f(x) changes as x approaches infinity, whether positive or negative.

Calculus Vocabulary
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Definition--Calculus Topics--Continuous Functions

Definition--Calculus Topics--Continuous Functions

A function is continuous if it has no gaps along the domain of the function.

Calculus Vocabulary
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Definition--Calculus Topics--Absolute Minimum

Definition--Calculus Topics--Absolute Minimum

When a function takes an input value, a, for some value in the domain, such that f(a) ≤ f(x), for all x in the domain.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Local Minimum

Definition--Calculus Topics--Local Minimum

When a function takes an input value, a, for some region in the domain, such that f(a) ≤ f(x), for all x in that region.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Acceleration

Definition--Calculus Topics--Acceleration

The second derivative, with respect to time, for the displacement function. Acceleration is a vector quantity.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Floor Function

Definition--Calculus Topics--Floor Function

A discrete function that takes real number values and whose output is the greatest integer value greater than the input value. The graph looks like a staircase.

Calculus Vocabulary
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Definition--Calculus Topics--Displacement Function

Definition--Calculus Topics--Displacement Function

A distance-vs.-time function used to find the distance an object has moved from a starting point.

Calculus Vocabulary
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Definition--Calculus Topics--One-Sided Limits

Definition--Calculus Topics--One-Sided Limits

Restricting the limit of a function for values approaching the limiting value from one side.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Ceiling Function

Definition--Calculus Topics--Ceiling Function

A discrete function that takes real number values and whose output is the least integer value greater than the input value. The graph looks like a staircase.

Calculus Vocabulary
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Definition--Calculus Topics--Power Rule

Definition--Calculus Topics--Power Rule

The process of finding the derivative of a power function.

Calculus Vocabulary
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Definition--Calculus Topics--Derivative of a Linear Function

Definition--Calculus Topics--Derivative of a Linear Function

The derivative of a linear function of the form y = mx + b is the slope of the line, m.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Second Derivative

Definition--Calculus Topics--Second Derivative

For differentiable function f(x), the second derivative is the derivative of f'(x) and denoted as f''(x).

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Convex Function

Definition--Calculus Topics--Convex Function

A function whose graph curves up along an interval of the domain. The inflection point is where the first derivative is zero.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Derivative of an Exponential Function

Definition--Calculus Topics--Derivative of an Exponential Function

The derivative of an exponential function is the product of the function and the natural log of the base. The derivative of ex is ex.

Calculus Vocabulary
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Definition--Calculus Topics--Derivative of a Composite Function

Definition--Calculus Topics--Derivative of a Composite Function

For two functions f(x) and g(x), the derivative of the composite function f(g(x)) is f'(x)*g'(x). This is an example of the Chain Rule.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Parametric Equations

Definition--Calculus Topics--Parametric Equations

A set of equations where each variable, x and y, is a function of a third variable, t. Graphs of parametric equations are sometimes not functions.

Calculus Vocabulary
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Definition--Calculus Topics--Sigma Notation

Definition--Calculus Topics--Sigma Notation

The Greek letter used for summarizing terms of a finite or infinite sequence.

Calculus Vocabulary
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Definition--Calculus Topics--Derivative of a Polynomial Function

Definition--Calculus Topics--Derivative of a Polynomial Function

The derivative of a polynomial of degree n is another polynomial of degree n - 1.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Rolle's Theorem

Definition--Calculus Topics--Rolle's Theorem

For function f(x) along an interval [a, b], if f(a) = f(b), then there is a point along the interval where the derivative is zero.

Calculus Vocabulary
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Definition--Calculus Topics--Zeros of a Function

Definition--Calculus Topics--Zeros of a Function

Where the graph of a function intersects the x-axis. The solutions to the equation f(x) = 0 for some function f(x).

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Vector

Definition--Calculus Topics--Vector

A quantity that has magnitude and direction. Vectors are often used to model real-world phenomena such as force, speed, or acceleration.

Calculus Vocabulary
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Definition--Calculus Topics--Limits at Infinity

Definition--Calculus Topics--Limits at Infinity

Finding the limiting value for function f(x) as the input value x approaches infinity. This limit may or may not exist.

Calculus Vocabulary
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Definition--Calculus Topics--Composite Function

Definition--Calculus Topics--Composite Function

A function whose input values are made up of another function. For two functions f(x) and g(x), a composite function can be written as f(g(x)).

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Instantaneous Rate of Change

Definition--Calculus Topics--Instantaneous Rate of Change

Another way of describing the slope of the line tangent to a given curve at a given point.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Derivative of a Quadratic Function

Definition--Calculus Topics--Derivative of a Quadratic Function

Since a quadratic function is a polynomial function of degree 2, the derivative is a linear function.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Separable Differential Equation

Definition--Calculus Topics--Separable Differential Equation

A special type of differential equation in which functions f(x) and g(y) can be separated to find the solution to the equation.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Fundamental Theorem of Calculus

Definition--Calculus Topics--Fundamental Theorem of Calculus

The theorem that relates differentiation and integration. The two operations are basically inverses of each other.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Indefinite Integral

Definition--Calculus Topics--Indefinite Integral

The integral of a function without a specific limit on the endpoints. The result of an indefinite integral is a differentiable function.

Calculus Vocabulary
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Definition--Calculus Topics--Explicit Function

Definition--Calculus Topics--Explicit Function

A function in which y can be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equation.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Quotient Rule

Definition--Calculus Topics--Quotient Rule

The rule for finding the derivative of a function made up of the ratios of two functions f(x) and g(x).

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Derivative of a Rational Function

Definition--Calculus Topics--Derivative of a Rational Function

Since a rational function is the ratio of two polynomials, the derivative of a rational function is also the ratio of two polynomials.

Calculus Vocabulary
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Definition--Calculus Topics--First Derivative

Definition--Calculus Topics--First Derivative

For differentiable function f(x), the first derivative is denoted as f'(x).

Calculus Vocabulary
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Definition--Calculus Topics--Velocity

Definition--Calculus Topics--Velocity

The first derivative, with respect to time, for the displacement function. Velocity is a vector quantity.

Calculus Vocabulary
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Definition--Calculus Topics--Extreme Value Theorem

Definition--Calculus Topics--Extreme Value Theorem

For function f(x) along an interval, there are maximum and minimum values. If the derivative is zero along this interval, this is an inflection point.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--L'Hopital's Rule

Definition--Calculus Topics--L'Hopital's Rule

For function f(x)/g(x), where f(x) and g(x) are two functions, along an interval [a, b], if there is a point c in the interval such that g(x) = 0, then L'Hopital'

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Chain Rule

Definition--Calculus Topics--Chain Rule

The process for finding the derivative of a composite function.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Discrete Function

Definition--Calculus Topics--Discrete Function

A function whose graphs has gaps. This is because the function consists of separate ordered pairs or is a discontinuous function with gaps.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Vertical Asymptote

Definition--Calculus Topics--Vertical Asymptote

A vertical line that the graph of a function approaches but does not intersect. The equation of a vertical asymptote is x = c, for some constant c.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Integral

Definition--Calculus Topics--Integral

A method for finding the area of a curve along an interval. In calculus, integrating a function f(x) involves finding the antiderivative of f(x).

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Differentiable Function

Definition--Calculus Topics--Differentiable Function

A function is differentiable if a derivative can be found at each point in its domain.

Calculus Vocabulary
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Definition--Calculus Topics--Piecewise Function

Definition--Calculus Topics--Piecewise Function

A function made up of separate functions, each with its own interval.

Calculus Vocabulary
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Definition--Calculus Topics--Change of Variables

Definition--Calculus Topics--Change of Variables

A substitution technique where a variable replaces a more complicated expression. In calculus it can simplify differentiation or integration.

Calculus Vocabulary
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Definition--Calculus Topics--Oblique Asymptote

Definition--Calculus Topics--Oblique Asymptote

A slanted line that the graph of a function approaches but does not intersect.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Intermediate Value Theorem

Definition--Calculus Topics--Intermediate Value Theorem

For continuous function f(x) along interval [a, b] there are values between f(a) and f(b).

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Derivative of a Trig Function

Definition--Calculus Topics--Derivative of a Trig Function

The derivative of a trig function is another trig function, as shown in the table.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Odd Function

Definition--Calculus Topics--Odd Function

A function whose graph has point symmetry about the origin.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Left-Hand Limit

Definition--Calculus Topics--Left-Hand Limit

As a function f(x) approaches a specific input value a, for x-values less than or equal to a, the function may approach a specific limiting value.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Derivative

Definition--Calculus Topics--Derivative

A function used to find the slope of a tangent to a curve at a given point. The derivative is based on the following limit.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Integral Symbol

Definition--Calculus Topics--Integral Symbol

The mathematical symbol used to denote the process of integration.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Integration by Substitution

Definition--Calculus Topics--Integration by Substitution

Replacing the integrand with a simpler expression to make the process of integration easier.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Trig Identities

Definition--Calculus Topics--Trig Identities

Equations that involve trigonmetric functions and are often used to simplify certain trigonometric expressions.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Inverse Function

Definition--Calculus Topics--Inverse Function

For function f(x), the inverse function f-1(x), if it exists, undoes the mapping of the original function.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Power Function

Definition--Calculus Topics--Power Function

A function with a single term that consists of a variable base raised to a real number power. The variable can also have a real number coefficient.

Calculus Vocabulary
PC.F.5.5

Definition--Calculus Topics--Definite Integral

Definition--Calculus Topics--Definite Integral

The integral of a function with specific limits on the endpoints. A definite integral results in a numerical value.

Calculus Vocabulary
PC.F.5.4

Math Definitions Collection--Calculus Concepts

This collection aggregates all the definitions for key terms in a standards Calculus course. There are a total of 88 images. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation. Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Discontinuous Function

Definition--Calculus Topics--Discontinuous Function

A function is discontinuous if it has one or more gaps along the domain of the function. The left- or right-hand limits exist but are not equal.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Linear Approximation

Definition--Calculus Topics--Linear Approximation

For differentiable function f(x), the linear approximation at x = a, for some real number a, is the equation of the line tangent to f(x) at a.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Tangent to a Curve

Definition--Calculus Topics--Tangent to a Curve

A line that intersects a curve at a single point and is perpendicular to the curve at that point.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative of a Quadratic Function

Definition--Calculus Topics--Derivative of a Quadratic Function

Since a quadratic function is a polynomial function of degree 2, the derivative is a linear function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Inflection Point

Definition--Calculus Topics--Inflection Point

The point on a curve where the curvature changes. This is often indicated by a change in the slopes of tangents to the curve.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Riemann Sum

Definition--Calculus Topics--Riemann Sum

An approximation method for estimating the area under a curve and used to approximate the solution to a definite integral.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Composite Function

Definition--Calculus Topics--Composite Function

A function whose input values are made up of another function. For two functions f(x) and g(x), a composite function can be written as f(g(x)).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative of an Exponential Function

Definition--Calculus Topics--Derivative of an Exponential Function

The derivative of an exponential function is the product of the function and the natural log of the base. The derivative of ex is ex.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Step Function

Definition--Calculus Topics--Step Function

A discontinuous function whose graph looks like a staircase. A step function can be generated by ceiling or floor functions.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Absolute Minimum

Definition--Calculus Topics--Absolute Minimum

When a function takes an input value, a, for some value in the domain, such that f(a) ≤ f(x), for all x in the domain.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative of a Linear Function

Definition--Calculus Topics--Derivative of a Linear Function

The derivative of a linear function of the form y = mx + b is the slope of the line, m.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Quotient Rule

Definition--Calculus Topics--Quotient Rule

The rule for finding the derivative of a function made up of the ratios of two functions f(x) and g(x).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Ceiling Function

Definition--Calculus Topics--Ceiling Function

A discrete function that takes real number values and whose output is the least integer value greater than the input value. The graph looks like a staircase.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--L'Hopital's Rule

Definition--Calculus Topics--L'Hopital's Rule

For function f(x)/g(x), where f(x) and g(x) are two functions, along an interval [a, b], if there is a point c in the interval such that g(x) = 0, then L'Hopital'

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Acceleration

Definition--Calculus Topics--Acceleration

The second derivative, with respect to time, for the displacement function. Acceleration is a vector quantity.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Area Beneath a Curve

Definition--Calculus Topics--Area Beneath a Curve

For a definite integral, it is the numerical result of the integration.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Antiderivative

Definition--Calculus Topics--Antiderivative

For two differentiable functions f(x) and F(x), if F'(x) = f(x), then F(x) is the antiderivative of f(x).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Implicit Differentiation

Definition--Calculus Topics--Implicit Differentiation

When a function cannot be written in the form of y as a function of x, then implicit differentation can be used to find the derivative with respect to x.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Extreme Value Theorem

Definition--Calculus Topics--Extreme Value Theorem

For function f(x) along an interval, there are maximum and minimum values. If the derivative is zero along this interval, this is an inflection point.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Concave Function

Definition--Calculus Topics--Concave Function

A function whose graph curves down along an interval of the domain. The inflection point is where the first derivative is zero.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Continuous Functions

Definition--Calculus Topics--Continuous Functions

A function is continuous if it has no gaps along the domain of the function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Absolute Maximum

Definition--Calculus Topics--Absolute Maximum

When a function takes an input value, a, for some value in the domain, such that f(a) ≥ f(x), for all x in the domain.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Right-Hand Limit

Definition--Calculus Topics--Right-Hand Limit

As a function f(x) approaches a specific input value a, for x-values greater than or equal to a, the function may approach a specific limiting value.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative of a Logarithmic Function

Definition--Calculus Topics--Derivative of a Logarithmic Function

The derivative of a logarithmic function uses the laws of logarithms and the definition of e to find the derivative.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Odd Function

Definition--Calculus Topics--Odd Function

A function whose graph has point symmetry about the origin.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Horizontal Asymptote

Definition--Calculus Topics--Horizontal Asymptote

A horizontal line that the graph of a function approaches but does not intersect. The equation of a horizontal asymptote is y = c, for some constant c.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Differentiable Function

Definition--Calculus Topics--Differentiable Function

A function is differentiable if a derivative can be found at each point in its domain.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Integral

Definition--Calculus Topics--Integral

A method for finding the area of a curve along an interval. In calculus, integrating a function f(x) involves finding the antiderivative of f(x).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Fundamental Theorem of Calculus

Definition--Calculus Topics--Fundamental Theorem of Calculus

The theorem that relates differentiation and integration. The two operations are basically inverses of each other.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Sigma Notation

Definition--Calculus Topics--Sigma Notation

The Greek letter used for summarizing terms of a finite or infinite sequence.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Even Function

Definition--Calculus Topics--Even Function

A function whose graph is symmetric about the y-axis.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Use implicit differentiation and the quotient rule to find the derivative of an inverse trig function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Rolle's Theorem

Definition--Calculus Topics--Rolle's Theorem

For function f(x) along an interval [a, b], if f(a) = f(b), then there is a point along the interval where the derivative is zero.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative of a Polynomial Function

Definition--Calculus Topics--Derivative of a Polynomial Function

The derivative of a polynomial of degree n is another polynomial of degree n - 1.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Sum Rule

Definition--Calculus Topics--Sum Rule

For differentiable functions f(x) and g(x) along a given interval, the derivative of the sum f(x) + g(x) is the sum of the individual derivatives f'(x) and g'(x).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative

Definition--Calculus Topics--Derivative

A function used to find the slope of a tangent to a curve at a given point. The derivative is based on the following limit.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Trapezoidal Rule

Definition--Calculus Topics--Trapezoidal Rule

A technique for approximating a definite integral by adding the areas of trapezoids underneath a curve.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--One-Sided Limits

Definition--Calculus Topics--One-Sided Limits

Restricting the limit of a function for values approaching the limiting value from one side.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Definite Integral

Definition--Calculus Topics--Definite Integral

The integral of a function with specific limits on the endpoints. A definite integral results in a numerical value.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Convex Function

Definition--Calculus Topics--Convex Function

A function whose graph curves up along an interval of the domain. The inflection point is where the first derivative is zero.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Integration by Substitution

Definition--Calculus Topics--Integration by Substitution

Replacing the integrand with a simpler expression to make the process of integration easier.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--End Behavior

Definition--Calculus Topics--End Behavior

The way a function f(x) changes as x approaches infinity, whether positive or negative.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative of a Trig Function

Definition--Calculus Topics--Derivative of a Trig Function

The derivative of a trig function is another trig function, as shown in the table.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Average Rates of Change

Definition--Calculus Topics--Average Rates of Change

The ratio along an interval of a domain for a given function, comparable to calculating the slope of a line.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Hooke's Law

Definition--Calculus Topics--Hooke's Law

A second-order differential equation that is used to model simple harmonic motion using a trigonometric function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Integrand

Definition--Calculus Topics--Integrand

In the process of integration, it is the function that is being integrated.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative of a Composite Function

Definition--Calculus Topics--Derivative of a Composite Function

For two functions f(x) and g(x), the derivative of the composite function f(g(x)) is f'(x)*g'(x). This is an example of the Chain Rule.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Indefinite Integral

Definition--Calculus Topics--Indefinite Integral

The integral of a function without a specific limit on the endpoints. The result of an indefinite integral is a differentiable function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Limits at Infinity

Definition--Calculus Topics--Limits at Infinity

Finding the limiting value for function f(x) as the input value x approaches infinity. This limit may or may not exist.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Floor Function

Definition--Calculus Topics--Floor Function

A discrete function that takes real number values and whose output is the greatest integer value greater than the input value. The graph looks like a staircase.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Mean Value Theorem

Definition--Calculus Topics--Mean Value Theorem

For differentiable function f(x) along the closed interval [a, b] there is a value c within that interval such that f'(c) is parallel to the secant formed by th

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Limit

Definition--Calculus Topics--Limit

As a function f(x) approaches a specific input value a, the function may approach a specific limiting value. This limit may or may not exist.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Power Rule

Definition--Calculus Topics--Power Rule

The process of finding the derivative of a power function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Piecewise Function

Definition--Calculus Topics--Piecewise Function

A function made up of separate functions, each with its own interval.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Differentiation

Definition--Calculus Topics--Differentiation

The process of finding the derivative of a function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Local Minimum

Definition--Calculus Topics--Local Minimum

When a function takes an input value, a, for some region in the domain, such that f(a) ≤ f(x), for all x in that region.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Zeros of a Function

Definition--Calculus Topics--Zeros of a Function

Where the graph of a function intersects the x-axis. The solutions to the equation f(x) = 0 for some function f(x).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Matrix Representations of Vectors

Definition--Calculus Topics--Matrix Representations of Vectors

A vector quantity can be represented by a matrix.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Delta y

Definition--Calculus Topics--Delta y

The change in y-coordinates for a given function. Often used in the formula for finding the derivative of a function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Displacement Function

Definition--Calculus Topics--Displacement Function

A distance-vs.-time function used to find the distance an object has moved from a starting point.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Second Derivative

Definition--Calculus Topics--Second Derivative

For differentiable function f(x), the second derivative is the derivative of f'(x) and denoted as f''(x).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Vector

Definition--Calculus Topics--Vector

A quantity that has magnitude and direction. Vectors are often used to model real-world phenomena such as force, speed, or acceleration.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Rational Function

Definition--Calculus Topics--Rational Function

A function made up of the ratio of two functions f(x) and g(x).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Intermediate Value Theorem

Definition--Calculus Topics--Intermediate Value Theorem

For continuous function f(x) along interval [a, b] there are values between f(a) and f(b).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Left-Hand Limit

Definition--Calculus Topics--Left-Hand Limit

As a function f(x) approaches a specific input value a, for x-values less than or equal to a, the function may approach a specific limiting value.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Trigonometric Function

Definition--Calculus Topics--Trigonometric Function

One of six main functions, including sine, cosine, tangent, secant, cosecant, and cotangent.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Change of Variables

Definition--Calculus Topics--Change of Variables

A substitution technique where a variable replaces a more complicated expression. In calculus it can simplify differentiation or integration.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Velocity

Definition--Calculus Topics--Velocity

The first derivative, with respect to time, for the displacement function. Velocity is a vector quantity.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Integral Symbol

Definition--Calculus Topics--Integral Symbol

The mathematical symbol used to denote the process of integration.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Delta x

Definition--Calculus Topics--Delta x

The change in x-coordinates for a given function. Often used in the formula for finding the derivative of a function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Derivative of a Rational Function

Definition--Calculus Topics--Derivative of a Rational Function

Since a rational function is the ratio of two polynomials, the derivative of a rational function is also the ratio of two polynomials.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Power Function

Definition--Calculus Topics--Power Function

A function with a single term that consists of a variable base raised to a real number power. The variable can also have a real number coefficient.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Implicit Function

Definition--Calculus Topics--Implicit Function

A function in which y cannot be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equatio

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Instantaneous Rate of Change

Definition--Calculus Topics--Instantaneous Rate of Change

Another way of describing the slope of the line tangent to a given curve at a given point.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Trig Identities

Definition--Calculus Topics--Trig Identities

Equations that involve trigonmetric functions and are often used to simplify certain trigonometric expressions.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Chain Rule

Definition--Calculus Topics--Chain Rule

The process for finding the derivative of a composite function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--First Derivative

Definition--Calculus Topics--First Derivative

For differentiable function f(x), the first derivative is denoted as f'(x).

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Vertical Asymptote

Definition--Calculus Topics--Vertical Asymptote

A vertical line that the graph of a function approaches but does not intersect. The equation of a vertical asymptote is x = c, for some constant c.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Local Maximum

Definition--Calculus Topics--Local Maximum

When a function takes an input value, a, for some region in the domain, such that f(a) ≥ f(x), for all x in that region.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Differential Equation

Definition--Calculus Topics--Differential Equation

An equation that includes the derivative of a function f(x) and the variable x.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Discrete Function

Definition--Calculus Topics--Discrete Function

A function whose graphs has gaps. This is because the function consists of separate ordered pairs or is a discontinuous function with gaps.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Inverse Function

Definition--Calculus Topics--Inverse Function

For function f(x), the inverse function f-1(x), if it exists, undoes the mapping of the original function.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Absolute Value Function

Definition--Calculus Topics--Absolute Value Function

A piecewise function whose simplest form is shown below. These functions are not differentiable at their vertex.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Parametric Equations

Definition--Calculus Topics--Parametric Equations

A set of equations where each variable, x and y, is a function of a third variable, t. Graphs of parametric equations are sometimes not functions.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Asymptote

Definition--Calculus Topics--Asymptote

A line that the graph of a function approaches but does not intersect. Asymptotes can be vertical, horizontal, or oblique.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Separable Differential Equation

Definition--Calculus Topics--Separable Differential Equation

A special type of differential equation in which functions f(x) and g(y) can be separated to find the solution to the equation.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Oblique Asymptote

Definition--Calculus Topics--Oblique Asymptote

A slanted line that the graph of a function approaches but does not intersect.

Calculus Vocabulary
PC.F.5.4

Definition--Calculus Topics--Explicit Function

Definition--Calculus Topics--Explicit Function

A function in which y can be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equation.

Calculus Vocabulary
PC.F.5.3

Math Video Collection: Texas Instruments Tutorial Videos

This collection aggregates all the math videos and resources in this series: Texas Instruments Tutorial Videos. There are a total of 266 resources. Rational Expressions, Sequences, Series, Polynomial Functions and Equations, Graphs of Quadratic Functions, Quadratic Equations and Functions, Solving Systems of Equations, Trig Expressions and Identities, Probability, Geometric Constructions with Triangles, Composite Functions, Geometric Constructions with Angles and Planes, Distance Formula, Data Analysis, Slope, Special Functions, Trigonometric Functions, Graphs of Exponential and Logarithmic Functions, Radical Functions and Equations, Rational Functions and Equations, Slope-Intercept Form, Coordinate Systems, Graphs of Linear Functions, Inequalities, Matrix Operations and Midpoint Formula
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 48

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions: Linear to Linear

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping one

Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 49

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions: Linear to Quadratic

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping a

Composite Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Trigonometric

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Trigonometric Composite Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Linear with Sliders

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Linear with Sliders Composite Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Logarithmic

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Logarithmic Composite Functions
PC.F.5.3

Closed Captioned Video: Composite Functions, Linear to Quartic

Closed Captioned Video: Composite Functions, Linear to Quartic Composite Functions
PC.F.5.3

Closed Captioned Video: Comp Functions, Lin to Polynomial

Closed Captioned Video: Comp Functions, Lin to Polynomial

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping one linear function to a polynomial function.

Composite Functions
PC.F.5.3

Closed Captioned Video: Comp Functions, Lin to Lin w Sliders

Closed Captioned Video: Comp Functions, Lin to Lin w Sliders

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping one linear function to another linear function using sliders.

Composite Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Rational

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Rational Composite Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions: Linear to Quadratic

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions: Linear to Quadratic Composite Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Cubic

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Cubic Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 43

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Polynomial

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping

Composite Functions
PC.F.5.3

Closed Captioned Video: Comp Functions, Lin to Rational

Closed Captioned Video: Comp Functions, Lin to Rational

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping one linear function to a rational function.

Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 39

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Cubic

In this TI Nspire tutorial for the TI-Nspire CAS, we explore composite fun

Composite Functions
PC.F.5.3

Closed Captioned Video: Composite Functions: Linear to Linear

Closed Captioned Video: Composite Functions: Linear to Linear Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 60

VIDEO: TI-Nspire Mini-Tutorial: Exploring Cosine Curve Properties Using Sliders

In this TI Nspire tutorialthe Graphing window is used to create a slider-based graph of a cosine curve to explore its properties

Trigonometric Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Quartic

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Quartic Composite Functions
PC.F.5.3

Closed Captioned Video: Comp Functions, Lin to Exponential

Closed Captioned Video: Comp Functions, Lin to Exponential

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping one linear function toan exponential function.

Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 67

VIDEO: TI-Nspire Mini-Tutorial: Exploring Sine Curve Properties Using Sliders

In this TI Nspire tutorialthe Graphing window is used to create a slider-based graph of a sine curve to explore its properties.

Trigonometric Functions
PC.F.5.3

Closed Captioned Video: Composite Functions, Linear to Cubic

Closed Captioned Video: Composite Functions, Linear to Cubic Composite Functions
PC.F.5.3

Closed Captioned Video: Comp Functions, Lin to Logarithmic

Closed Captioned Video: Comp Functions, Lin to Logarithmic

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping one linear function to a logarithmic function.

Composite Functions
PC.F.5.3

Closed Captioned Video: Comp Functions, Lin to Trigonometric

Closed Captioned Video: Comp Functions, Lin to Trigonometric

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping one linear function to a trigonometric function.

Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 45

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Radical

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping one

Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 47

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Trigonometric

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mappi

Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 46

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Rational

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping on

Composite Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions: Linear to Linear

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions: Linear to Linear

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Composite Functions: Linear to Linear.

Composite Functions
PC.F.5.3

Closed Captioned Video: Composite Functions, Linear to Radical

Closed Captioned Video: Composite Functions, Linear to Radical Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 41

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Linear with Sliders

In this TI Nspire tutorial for the TI-Nspire CAS, we explore

Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 40

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Exponential

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping

Composite Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Polynomial

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Polynomial Composite Functions
PC.F.5.3

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Radical

Video Transcript: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Radical Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 69

VIDEO: TI-Nspire Mini-Tutorial: Finding the Intersection Point of Two Graphs

In this TI Nspire tutorial, the Graph window is used to graph two functions and finding the point of intersection.

Coordinate Systems
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 42

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Logarithmic

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping

Composite Functions
PC.F.5.3

Closed Captioned Video: Comp Functions: Lin to Quadratic

Closed Captioned Video: Comp Functions: Lin to Quadratic

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping a linear function to a quadratic.

Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 44

VIDEO: TI-Nspire Mini-Tutorial: Composite Functions, Linear to Quartic

In this TI Nspire tutorial for the TI-Nspire CAS, we explore mapping one

Composite Functions
PC.F.5.3

VIDEO: Ti-Nspire Mini-Tutorial, Video 59

VIDEO: TI-Nspire Mini-Tutorial: Exploring Composite Functions Composite Functions
PC.F.5.1

Math Definitions Collection--Calculus Concepts

This collection aggregates all the definitions for key terms in a standards Calculus course. There are a total of 88 images. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation. Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--Continuous Functions

Definition--Calculus Topics--Continuous Functions

A function is continuous if it has no gaps along the domain of the function.

Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--Concave Function

Definition--Calculus Topics--Concave Function

A function whose graph curves down along an interval of the domain. The inflection point is where the first derivative is zero.

Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--Integrand

Definition--Calculus Topics--Integrand

In the process of integration, it is the function that is being integrated.

Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--Integration by Substitution

Definition--Calculus Topics--Integration by Substitution

Replacing the integrand with a simpler expression to make the process of integration easier.

Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--End Behavior

Definition--Calculus Topics--End Behavior

The way a function f(x) changes as x approaches infinity, whether positive or negative.

Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--Discrete Function

Definition--Calculus Topics--Discrete Function

A function whose graphs has gaps. This is because the function consists of separate ordered pairs or is a discontinuous function with gaps.

Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--Differentiation

Definition--Calculus Topics--Differentiation

The process of finding the derivative of a function.

Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--Displacement Function

Definition--Calculus Topics--Displacement Function

A distance-vs.-time function used to find the distance an object has moved from a starting point.

Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--Discontinuous Function

Definition--Calculus Topics--Discontinuous Function

A function is discontinuous if it has one or more gaps along the domain of the function. The left- or right-hand limits exist but are not equal.

Calculus Vocabulary
PC.F.5.1

Definition--Calculus Topics--Composite Function

Definition--Calculus Topics--Composite Function

A function whose input values are made up of another function. For two functions f(x) and g(x), a composite function can be written as f(g(x)).

Calculus Vocabulary