Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 6: Even More Graphs of Functions

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Collection Quadratics Collection: Texas Instruments Graphing Calculator Resources  

A set of resources for the TI-Nspire, TI-Nspire CX, and the Nspire App.

 

Applications of Quadratic Functions, Graphs of Quadratic Functions, Quadratic Formula, Data Analysis, Quadratic Equations and Functions, Inequalities and Composite Functions
Collection Quadratics Collection: Instructional Resources  

Here is a collection of PowerPoint presentations on selected topics in Quadratics.

 

Quadratic Equations and Functions, Applications of Quadratic Functions, Graphs of Quadratic Functions, Numerical and Algebraic Expressions and Quadratic Formula
Math Examples Math Examples Collection: Graphical Solutions to Rational Equations

Overview

This collection aggregates a set of math examples on the topic of Graphical Solutions to Rational Equations. There are 10 examples.

 

Rational Functions and Equations
Functions Collection Math Definitions Collection: Functions and Relations

Overview

The "Functions and Relations" collection from Media4Math provides a comprehensive set of definitions essential for understanding key mathematical concepts. This collection includes terms such as domain, range, function, relation, inverse function, and composite function. These definitions are crucial for students as they form the foundation for more advanced topics in mathematics, such as calculus and algebra.

Special Functions, Composite Functions, Conic Sections, Relations and Functions and Functions and Their Inverses
Math Clip Art Math Clip Art Collection: Graphs of Linear Functions

Overview

This collection aggregates all the math clip art around the topic of Graphs of Linear Functions. There are a total of 10 images. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation.

 

To download the full set of these resources, click on this link.

 

Graphs of Linear Functions and Slope-Intercept Form
Collection Math Quiz Collection: Graphs of Linear Functions

Overview

This collection aggregates all the math quizzes on this topic: Graphs of Linear Functions. There are a total of 60 resources. This collection of quizzes is made up of downloadable PDFs. To download the full set of these resources, click on this link.

 

Graphs of Linear Functions and Slope-Intercept Form
Math Videos Math Video Collection: Video Tutorials Series: Linear Functions

Overview

This collection aggregates all the math videos and resources in this series: Video Tutorials Series: Linear Functions. There are a total of 18 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

Graphs of Linear Functions
Math Videos Math Video Collection: Algebra Applications Video Series: Linear Functions

Overview

This collection aggregates all the math videos and resources in this series: Algebra Applications Video Series: Linear Functions. There are a total of 26 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

Special Functions, Applications of Linear Functions and Graphs of Linear Functions
Math Videos Math Video Collection: Algebra Applications Video Series: Functions and Relations

Overview

This collection aggregates all the math videos and resources in this series: Algebra Applications Video Series: Functions and Relations. There are a total of 26 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

Applications of Functions and Relations, Conic Sections, Relations and Functions, Quadratic Equations and Functions and Geometric Constructions with Circles
Math Worksheets Math Worksheet Collection: Linear Functions in Tabular and Graph Form

Overview

This collection aggregates all the math worksheets around the topic of Linear Functions in Tabular and Graph Form. There are a total of 101 worksheets. Each worksheet includes an answer key. This collection of resources is made up of downloadable PDF files that you can easily incorporate into your instruction.

 

Graphs of Linear Functions and Applications of Linear Functions
Math Examples Math Examples Collection: Graphs of Rational Functions

Overview

This collection of 28 math examples focuses on the topic of Graphs of Rational Functions, offering a comprehensive resource for students and educators alike. The examples cover a wide range of skills and concepts related to rational functions, progressively increasing in complexity to challenge learners at various levels of understanding.

Rational Functions and Equations
Collection Measures of Central Tendency: Basic Terms and Definitions

 

Here we gather key terms, definitions, and formulas around Measures of Central Tendency.

 

Data Analysis and Relations and Functions
Collection Linear Functions and Equations Collection: Promethean Flipcharts This is a collection of Promethean Flipcharts that focus on Linear Functions and Equations. Applications of Linear Functions
Collection Linear Functions and Equations Collection: Texas Instruments Graphing Calculator Resources This is a collection of TI resources on the topic of Linear Functions and Equations. Graphs of Linear Functions, Slope-Intercept Form and Slope
Collection Functions and Relations Collection: Basic Definitions Here are key terms in the topic of Functions and Relations. Relations and Functions and Conic Sections
Collection Linear Functions and Equations Collection: Video Tutorials

Overview

This collection of videos analyzes linear functions in slope-intercept form. There are a total of 18 videos. 

 

Graphs of Linear Functions, Standard Form, Point-Slope Form, Slope, Special Functions and Applications of Linear Functions
Collection Linear Functions and Equations Collection: Algebra Applications Videos Real-world applications of linear functions and equations through this video series. Special Functions and Applications of Linear Functions
Closed Captioned Video:  Algebra Applications: Linear Functions, Segment 2: Cycling Closed Captioned Video: Algebra Applications: Linear Functions, Segment 2: Cycling Closed Captioned Video: Algebra Applications: Linear Functions, Segment 2: Cycling

Topic

Linear Functions

Description

Applies linear functions to cycling, calculating hill grades and distances using slope formulas and graphing.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Special Functions and Applications of Linear Functions
Closed Captioned Video: TI-Nspire Mini-Tutorial: Graphing a Linear Function Closed Captioned Video: Linear Function Closed Captioned Video: Linear Function

In this TI Nspire tutorial, the Graph window is used to graph a linear function. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet.

This is part of a collection of closed captioned videos on various math topics. To see the complete collection of the videos, click on this link. Note: The download is Media4Math's guide to closed captioned videos.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Video Transcripts

This video has a transcript available. To see the complete collection of video transcripts, click on this link.
Graphs of Linear Functions
Closed Captioned Video: TI-Nspire Mini-Tutorial: Graphing a Linear Inequality Using Sliders Closed Captioned Video: Linear Inequality Using Sliders Closed Captioned Video: Linear Inequality Using Sliders

In this TI Nspire tutorial, the Graph window is used to graph a linear inequality in slope-intercept form using sliders. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet.

Inequalities
Closed Captioned Video: Algebra Applications: Linear Functions Closed Captioned Video: Algebra Applications: Linear Functions Closed Captioned Video: Algebra Applications: Linear Functions

Topic

Linear Functions

Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Applications: Linear Functions, Segment 3: Oil Exploration Closed Captioned Video: Algebra Applications: Linear Functions, 3 Closed Captioned Video: Algebra Applications: Linear Functions, 3

Topic

Linear Functions

Description

Uses linear regression to analyze US oil consumption trends, projecting future usage and potential impact of Alaskan oil production.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Applications: Linear Functions, Segment 4: Exercise Closed Captioned Video: Algebra Applications: Linear Functions, 4 Closed Captioned Video: Algebra Applications: Linear Functions, 4

Topic

Linear Functions

Description

Models maximum heart rate during aerobic exercise with linear equations, creating exercise charts for various age groups.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Special Functions and Applications of Linear Functions
Closed Captioned Video: TI-Nspire Mini-Tutorial: Exploring the Slope-Intercept form Using Sliders Closed Captioned Video: Exp the Slope-Intercept form Closed Captioned Video: Exp the Slope-Intercept form

In this TI Nspire tutorial, the Graph window is used to create a slider-based graph of a linear function in slope-intercept form. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

Slope-Intercept Form
Closed Captioned Video: Linear Functions: Negative Slope, Negative y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Negative y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Negative y-Intercept

Video Tutorial: Linear Functions: Negative Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a negative y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Negative Slope, Positive y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Positive y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Positive y-Intercept

Video Tutorial: Linear Functions: Negative Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a positive y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Negative Slope, Zero y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Zero y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Zero y-Intercept

Video Tutorial: Linear Functions: Negative Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a zero y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Positive Slope, Negative y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Negative y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Negative y-Intercept

Video Tutorial: Linear Functions: Positive Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a negative y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Positive Slope, Positive y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Positive y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Positive y-Intercept

Video Tutorial: Linear Functions: Positive Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a positive y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Positive Slope, Zero y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Zero y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Zero y-Intercept

Video Tutorial: Linear Functions: Positive Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a zero y-intercept.

Graphs of Linear Functions
Definition--Functions and Relations Concepts--Absolute Value Function Definition--Functions and Relations Concepts--Absolute Value Function Absolute Value Function

 

 

Topic

Functions and Relations

Definition

An absolute value function is a function that contains an algebraic expression within absolute value symbols. It is defined as 

$$ f(x) = |x| $$

where |x| denotes the absolute value ofx.

Description

The absolute value function is significant in mathematics because it measures the distance of a number from zero on the number line, regardless of direction. This function is linear in nature, as it can be broken into two linear pieces: one for 

$$ x \geq 0 $$

 and one for 

$$ x < 0 $$

Special Functions
Definition--Functions and Relations Concepts--Composite Function Definition--Functions and Relations Concepts--Composite Function Composite Function

Topic

Functions and Relations

Definition

A composite function is a function that is formed when one function is applied to the result of another function.

Description

Composite functions are significant in mathematics because they allow the combination of two functions to form a new function. This is denoted as (f∘g)(x) = f(g(x)). Composite functions are widely used in various fields, including computer science for function composition in programming and in calculus for chain rule applications. For example, if f(x) = 2x and g(x) = x + 3, then the composite function 

(f∘g)(x) = f(g(x)) = 2(x + 3) = 2x+6

Composite Functions
Definition--Functions and Relations Concepts--Conic Sections Definition--Functions and Relations Concepts--Conic Sections Conic Sections

Topic

Functions and Relations

Definition

Conic sections are the curves obtained by intersecting a plane with a double-napped cone.

Description

Conic sections include circles, ellipses, parabolas, and hyperbolas, which are fundamental in the study of geometry and algebra. These shapes are described by quadratic equations and have numerous applications in physics, engineering, and astronomy. For example, the orbits of planets are ellipses, and parabolic mirrors are used in telescopes and satellite dishes. The general quadratic equation for conic sections is 

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

Conic Sections
Definition--Functions and Relations Concepts--Constant Function Definition--Functions and Relations Concepts--Constant Function Constant Function

Topic

Functions and Relations

Definition

A constant function is a function that always returns the same value, no matter the input.

Description

The constant function is one of the simplest types of functions in mathematics, expressed as 

f(x) = c

Relations and Functions
Definition--Functions and Relations Concepts--Continuous Function Definition--Functions and Relations Concepts--Continuous Function Continuous Function

Topic

Functions and Relations

Definition

A continuous function is a function that does not have any breaks, holes, or gaps in its domain.

Description

Continuous functions are fundamental in calculus and mathematical analysis because they allow for the application of limits, derivatives, and integrals. A function f(x) is continuous if, for every point 𝑐 c in its domain, 

lim x→c ​ f(x) = f(c)

Relations and Functions
Definition--Functions and Relations Concepts--Decreasing Function Definition--Functions and Relations Concepts--Decreasing Function Decreasing Function

Topic

Functions and Relations

Definition

A decreasing function is a function where the value of the function decreases as the input increases.

Description

Decreasing functions are important in mathematics because they describe scenarios where an increase in one variable leads to a decrease in another. This is mathematically represented as 

f(x1) > f(x2) for any đ‘„1 < đ‘„2 ​

Relations and Functions
Definition--Functions and Relations Concepts--Dependent Variable Definition--Functions and Relations Concepts--Dependent Variable Dependent Variable

Topic

Functions and Relations

Definition

A dependent variable is a variable whose value depends on one or more other variables.

Relations and Functions
Definition--Functions and Relations Concepts--Discontinuous Function Definition--Functions and Relations Concepts--Discontinuous Function Discontinuous Function

Topic

Functions and Relations

Definition

A discontinuous function is a function that has one or more points where it is not continuous.

Relations and Functions
Definition--Functions and Relations Concepts--Discrete Functions Definition--Functions and Relations Concepts--Discrete Functions Discrete Functions

Topic

Functions and Relations

Definition

Discrete functions are functions that are defined only for a set of discrete points.

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

Topic

Functions and Relations

Definition

Distorting a function horizontally involves stretching or compressing the graph of the function along the x-axis.

Description

Horizontal distortions of functions are significant because they alter the input values while maintaining the overall shape of the graph. This is mathematically represented as 

f(kx)

where k is a constant. If k > 1, the function compresses horizontally, and if 0 < 𝑘 < 1, it stretches. 

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

Topic

Functions and Relations

Definition

Distorting a function vertically involves stretching or compressing the graph of the function along the y-axis.

Description

Vertical distortions of functions are significant because they alter the output values while maintaining the overall shape of the graph. This is mathematically represented as 

kf(x)

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

Topic

Functions and Relations

Definition

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Relations and Functions
Definition--Functions and Relations Concepts--Even Function Definition--Functions and Relations Concepts--Even Function Even Function

Topic

Functions and Relations

Definition

An even function is a function that satisfies the condition f(x) = f(−x) for all x in its domain.

Description

Even functions are important in mathematics because they exhibit symmetry about the y-axis. This property is useful in various fields, including physics and engineering, where symmetry simplifies analysis and problem-solving. For example, the function 

f(x)=x2

Relations and Functions
Definition--Functions and Relations Concepts--Function Definition--Functions and Relations Concepts--Function Function

Topic

Functions and Relations

Definition

A function is a relation that uniquely associates each element of a set with exactly one element of another set.

Relations and Functions
Definition--Functions and Relations Concepts--Function Machine Definition--Functions and Relations Concepts--Function Machine Function Machine

Topic

Functions and Relations

Definition

A function machine is a conceptual tool used to understand how functions work by visualizing inputs and outputs.

Description

The function machine is a useful educational tool that helps students grasp the concept of functions by visualizing the process of converting inputs into outputs. It emphasizes the idea that a function takes an input, processes it according to a specific rule, and produces an output. For example, if the function is 

f(x) = x + 2

Relations and Functions
Definition--Functions and Relations Concepts--Function Notation Definition--Functions and Relations Concepts--Function Notation Function Notation

Topic

Functions and Relations

Definition

Function notation is a way to represent functions in the form f(x), where f denotes the function and x denotes the input variable.

Description

Function notation is a standardized way to write functions, making it easier to understand and communicate mathematical relationships. It is widely used in algebra, calculus, and other branches of mathematics. For example, the notation 

f(x) = x2 

Relations and Functions
Definition--Functions and Relations Concepts--Function Table Definition--Functions and Relations Concepts--Function Table Function Table

Topic

Functions and Relations

Definition

A function table is a table that lists input values and their corresponding output values for a given function.

Description

Function tables are useful tools in mathematics for organizing and analyzing the relationship between inputs and outputs of a function. They help in visualizing how a function behaves and in identifying patterns. For example, a function table for 

f(x) = 2x + 1

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

Topic

Functions and Relations

Definition

Graphs of functions are visual representations of the relationship between input values and output values of a function.

Description

Graphs of functions are essential tools in mathematics for visualizing how a function behaves. They provide a clear picture of the relationship between the input and output values, making it easier to analyze and interpret the function. For example, the graph of 

f(x) = x2 

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

Topic

Functions and Relations

Definition

Graphs of relations are visual representations of the relationship between two sets of values, not necessarily functions.

Relations and Functions
Definition--Functions and Relations Concepts--Increasing Function Definition--Functions and Relations Concepts--Increasing Function Increasing Function

Topic

Functions and Relations

Definition

An increasing function is a function where the value of the function increases as the input increases.

Relations and Functions