These are the resources that support this Florida Standard.
MAFS.912.F-BF.1.1: Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a
constant function to a decaying exponential, and relate these functions to the model.
c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
There are 285 resources.
| Title | Description | Thumbnail Image | Curriculum Topics |
|---|---|---|---|
Closed Captioned Video: Quadratics: What Is a Quadratic Function? |
Closed Captioned Video: Quadratics: What Is a Quadratic Function?Video Tutorial: Quadratics: What Is a Quadratic Function? In this video, students learn about the characteristics of quadratic functions by looking at data, graphs, and equations. This video works with quadratic functions in standard form. |
|
Graphs of Quadratic Functions and Quadratic Equations and Functions |
Definition--Calculus Topics--Absolute Maximum |
Definition--Calculus Topics--Absolute MaximumWhen 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 |
Definition--Calculus Topics--Absolute Minimum |
Definition--Calculus Topics--Absolute MinimumWhen 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 |
Definition--Calculus Topics--Absolute Value Function |
Definition--Calculus Topics--Absolute Value FunctionA piecewise function whose simplest form is shown below. These functions are not differentiable at their vertex. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Acceleration |
Definition--Calculus Topics--AccelerationThe second derivative, with respect to time, for the displacement function. Acceleration is a vector quantity. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Antiderivative |
Definition--Calculus Topics--AntiderivativeFor two differentiable functions f(x) and F(x), if F'(x) = f(x), then F(x) is the antiderivative of f(x). |
|
Calculus Vocabulary |
Definition--Calculus Topics--Area Beneath a Curve |
Definition--Calculus Topics--Area Beneath a CurveFor a definite integral, it is the numerical result of the integration. For an indefinite integral, it is the resulting function from the integration for calculating the area. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Asymptote |
Definition--Calculus Topics--AsymptoteA line that the graph of a function approaches but does not intersect. Asymptotes can be vertical, horizontal, or oblique. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Average Rates of Change |
Definition--Calculus Topics--Average Rates of ChangeThe ratio along an interval of a domain for a given function, comparable to calculating the slope of a line. The average rate of change is found using this formula. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Ceiling Function |
Definition--Calculus Topics--Ceiling FunctionA 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 |
Definition--Calculus Topics--Chain Rule |
Definition--Calculus Topics--Chain RuleThe process for finding the derivative of a composite function. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Change of Variables |
Definition--Calculus Topics--Change of VariablesA substitution technique where a variable replaces a more complicated expression. In calculus it can simplify differentiation or integration. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Composite Function |
Definition--Calculus Topics--Composite FunctionA 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 |
Definition--Calculus Topics--Concave Function |
Definition--Calculus Topics--Concave FunctionA function whose graph curves down along an interval of the domain. The inflection point is where the first derivative is zero. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Continuous Functions |
Definition--Calculus Topics--Continuous FunctionsA function is continuous if it has no gaps along the domain of the function. For some value a in the domain of function f(x), the limit as x approaches a is f(a). |
|
Calculus Vocabulary |
Definition--Calculus Topics--Convex Function |
Definition--Calculus Topics--Convex FunctionA function whose graph curves up along an interval of the domain. The inflection point is where the first derivative is zero. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Definite Integral |
Definition--Calculus Topics--Definite IntegralThe integral of a function with specific limits on the endpoints. A definite integral results in a numerical value. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Delta x |
Definition--Calculus Topics--Delta xThe change in x-coordinates for a given function. Often used in the formula for finding the derivative of a function. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Delta y |
Definition--Calculus Topics--Delta yThe change in y-coordinates for a given function. Often used in the formula for finding the derivative of a function. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Derivative |
Definition--Calculus Topics--DerivativeA 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 |
Definition--Calculus Topics--Derivative of a Composite Function |
Definition--Calculus Topics--Derivative of a Composite FunctionFor 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 |
Definition--Calculus Topics--Derivative of a Linear Function |
Definition--Calculus Topics--Derivative of a Linear FunctionThe derivative of a linear function of the form y = mx + b is the slope of the line, m. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Derivative of a Logarithmic Function |
Definition--Calculus Topics--Derivative of a Logarithmic FunctionThe derivative of a logarithmic function uses the laws of logarithms and the definition of e to find the derivative. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Derivative of a Polynomial Function |
Definition--Calculus Topics--Derivative of a Polynomial FunctionThe derivative of a polynomial of degree n is another polynomial of degree n - 1. |
|
Calculus Vocabulary |
Definition--Calculus Topics--Derivative of a Quadratic Function |
Definition--Calculus Topics--Derivative of a Quadratic FunctionSince a quadratic function is a polynomial function of degree 2, the derivative is a linear function. |
|
Calculus Vocabulary |
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