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Unit: Functions

Evaluating functions

Learn
What is a function?
(Opens a modal)
Worked example: Evaluating functions from equation
(Opens a modal)
Worked example: Evaluating functions from graph
(Opens a modal)
Worked example: evaluating expressions with function notation
(Opens a modal)
Practice
Evaluate functions
4 questions
Evaluate functions from their graph
4 questions
Evaluate function expressions
4 questions

Inputs and outputs of a function

Learn
Worked example: matching an input to a function's output (equation)
(Opens a modal)
Worked example: matching an input to a function's output (graph)
(Opens a modal)
Worked example: two inputs with the same output (graph)
(Opens a modal)
Practice
Function inputs & outputs: equation
4 questions
Function inputs & outputs: graph
4 questions

Functions and equations

Learn
Equations vs. functions
(Opens a modal)
Obtaining a function from an equation
(Opens a modal)
Practice
Function rules from equations
4 questions

Interpreting function notation

Learn
Function notation word problem: bank
(Opens a modal)
Function notation word problem: beach
(Opens a modal)
Practice
Function notation word problems
4 questions

Introduction to the domain and range of a function

Learn
Intervals and interval notation
(Opens a modal)
What is the domain of a function?
(Opens a modal)
What is the range of a function?
(Opens a modal)
Worked example: domain and range from graph
(Opens a modal)
Practice
Domain and range from graph
7 questions

Determining the domain of a function

Learn
Domain of a radical function
(Opens a modal)
Worked example: domain of algebraic functions
(Opens a modal)
Worked example: determining domain word problem (real numbers)
(Opens a modal)
Worked example: determining domain word problem (positive integers)
(Opens a modal)
Worked example: determining domain word problem (all integers)
(Opens a modal)
Practice
Determine the domain of functions
4 questions
Function domain word problems
4 questions

Recognizing functions

Learn
Recognizing functions from graph
(Opens a modal)
Does a vertical line represent a function?
(Opens a modal)
Recognizing functions from table
(Opens a modal)
Recognizing functions from verbal description
(Opens a modal)
Recognizing functions from verbal description word problem
(Opens a modal)
Practice
Recognize functions from graphs
4 questions
Recognize functions from tables
4 questions

Piecewise functions

Learn
Introduction to piecewise functions
(Opens a modal)
Worked example: evaluating piecewise functions
(Opens a modal)
Worked example: graphing piecewise functions
(Opens a modal)
Worked example: domain & range of step function
(Opens a modal)
Worked example: domain & range of piecewise linear functions
(Opens a modal)
Practice
Evaluate piecewise functions
4 questions
Evaluate step functions
4 questions
Piecewise functions graphs
4 questions

Maximum and minimum points

Learn
Introduction to minimum and maximum points
(Opens a modal)
Worked example: absolute and relative extrema
(Opens a modal)
Practice
Relative maxima and minima
4 questions
Absolute maxima and minima
4 questions

Intervals where a function is positive, negative, increasing, or decreasing

Learn
Increasing, decreasing, positive or negative intervals
(Opens a modal)
Worked example: positive & negative intervals
(Opens a modal)
Practice
Positive and negative intervals
4 questions
Increasing and decreasing intervals
4 questions

Interpreting features of graphs

Learn
Graph interpretation word problem: temperature
(Opens a modal)
Graph interpretation word problem: basketball
(Opens a modal)
Practice
Graph interpretation word problems
4 questions

Average rate of change

Learn
Introduction to average rate of change
(Opens a modal)
Worked example: average rate of change from graph
(Opens a modal)
Worked example: average rate of change from table
(Opens a modal)
Worked example: average rate of change from equation
(Opens a modal)
Practice
Average rate of change: graphs & tables
4 questions
Average rate of change of polynomials
4 questions

Average rate of change word problems

Learn
Average rate of change word problem: table
(Opens a modal)
Average rate of change word problem: graph
(Opens a modal)
Average rate of change word problem: equation
(Opens a modal)
Average rate of change review
(Opens a modal)
Practice
Average rate of change word problems
4 questions

Combining functions

Learn
Intro to combining functions
(Opens a modal)
Adding functions
(Opens a modal)
Subtracting functions
(Opens a modal)
Adding and subtracting functions
(Opens a modal)
Multiplying functions
(Opens a modal)
Dividing functions
(Opens a modal)
Multiplying and dividing functions
(Opens a modal)

Composing functions (Algebra 2 level)

Learn
Intro to composing functions
(Opens a modal)
Intro to composing functions
(Opens a modal)
Composing functions
(Opens a modal)
Evaluating composite functions
(Opens a modal)
Evaluating composite functions: using tables
(Opens a modal)
Evaluating composite functions: using graphs
(Opens a modal)
Finding composite functions
(Opens a modal)
Evaluating composite functions (advanced)
(Opens a modal)
Practice
Evaluate composite functions
4 questions
Evaluate composite functions: graphs & tables
4 questions
Find composite functions
4 questions

Shifting functions

Learn
Shifting functions examples
(Opens a modal)
Graphing shifted functions
(Opens a modal)
Practice
Shift functions
4 questions

Stretching functions

Learn
Identifying function transformations
(Opens a modal)
Identifying horizontal squash from graph
(Opens a modal)
Reflecting & compressing functions
(Opens a modal)
Practice
Identify function transformations
4 questions

Modeling situations by combining and composing functions (Algebra 2 level)

Learn
Modeling with function combination
(Opens a modal)
Modeling with composite functions
(Opens a modal)
Modeling with composite functions (example 2)
(Opens a modal)
Practice
Model with function combination
4 questions
Model with composite functions
4 questions

Introduction to inverses of functions (Algebra 2 level)

Learn
Intro to inverse functions
(Opens a modal)
Intro to inverse functions
(Opens a modal)
Inputs & outputs of inverse functions
(Opens a modal)
Graphing the inverse of a linear function
(Opens a modal)
Practice
Evaluate inverse functions
4 questions

Finding inverse functions (Algebra 2 level)

Learn
Finding inverse functions: linear
(Opens a modal)
Finding inverse functions: quadratic
(Opens a modal)
Finding inverse functions: quadratic (example 2)
(Opens a modal)
Finding inverse functions: radical
(Opens a modal)
Finding inverses of rational functions
(Opens a modal)
Finding inverse functions
(Opens a modal)
Practice
Finding inverses of linear functions
4 questions

Verifying that functions are inverses (Algebra 2 level)

Learn
Verifying inverse functions by composition
(Opens a modal)
Verifying inverse functions by composition
(Opens a modal)
Verifying inverse functions by composition: not inverse
(Opens a modal)
Practice
Verify inverse functions
4 questions

Determining whether a function is invertible (Algebra 2 level)

Learn
Determining if a function is invertible
(Opens a modal)
Intro to invertible functions
(Opens a modal)
Restricting domains of functions to make them invertible
(Opens a modal)
Practice
Determine if a function is invertible
4 questions
Restrict domains of functions to make them invertible
4 questions

Determining the domain of advanced functions (Algebra 2 level)

Learn
Domain of advanced functions
(Opens a modal)
Practice
Domain of advanced functions
4 questions
Domain of advanced piecewise functions
4 questions

Determining the range of a function (Algebra 2 level)

Learn
Domain and range of quadratic functions
(Opens a modal)
Range of quadratic functions
(Opens a modal)
Practice
Range of quadratic functions
4 questions

Graphing nonlinear piecewise functions (Algebra 2 level)

Learn
Graphs of nonlinear piecewise functions
(Opens a modal)
Practice
Graphs of nonlinear piecewise functions
4 questions

Interpreting the symmetry of algebraic models (Algebra 2 level)

Learn
Symmetry of algebraic models
(Opens a modal)
Symmetry of algebraic models
(Opens a modal)

Interpreting the end behavior of algebraic models (Algebra 2 level)

Learn
End behavior of algebraic models
(Opens a modal)
Practice
End behavior of algebraic models
4 questions

Interpreting the periodicity of algebraic models (Algebra 2 level)

Learn
Periodicity of algebraic models
(Opens a modal)
Practice
Periodicity of algebraic models
4 questions

Comparing features of functions (Algebra 2 level)

Learn
Comparing functions: x-intercepts
(Opens a modal)
Comparing functions: shared features
(Opens a modal)
Comparing maximum points of quadratic functions
(Opens a modal)
Practice
Compare features of functions
4 questions

Two-variable functions

Learn
New operator definitions 1
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New operator definitions 2
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Practice
New operator definitions 1
4 questions
New operator definitions 2
4 questions

Unit test

Test your understanding of Functions with these 39 questions.

About this unit

This topic covers: - Evaluating functions - Domain & range of functions - Graphical features of functions - Average rate of change of functions - Function combination and composition - Function transformations (shift, reflect, stretch) - Piecewise functions - Inverse functions - Two-variable functions