# Functions

## Evaluating functions

Learn
What is a function?Worked example: Evaluating functions from equationWorked example: Evaluating functions from graphWorked example: evaluating expressions with function notation

## Inputs and outputs of a function

Learn
Worked example: matching an input to a function's output (equation)Worked example: matching an input to a function's output (graph)Worked example: two inputs with the same output (graph)

## Functions and equations

Learn
Equations vs. functionsObtaining a function from an equation

## Interpreting function notation

Learn
Function notation word problem: bankFunction notation word problem: beach

## Introduction to the domain and range of a function

Learn
Intervals and interval notationWhat is the domain of a function?What is the range of a function?Worked example: domain and range from graph
Practice

## Determining the domain of a function

Learn
Domain of a radical functionWorked example: domain of algebraic functionsWorked example: determining domain word problem (real numbers)Worked example: determining domain word problem (positive integers)Worked example: determining domain word problem (all integers)

## Recognizing functions

Learn
Recognizing functions from graphDoes a vertical line represent a function?Recognizing functions from tableRecognizing functions from verbal descriptionRecognizing functions from verbal description word problem

## Piecewise functions

Learn
Introduction to piecewise functionsWorked example: evaluating piecewise functionsWorked example: graphing piecewise functionsWorked example: domain & range of step functionWorked example: domain & range of piecewise linear functions

## Maximum and minimum points

Learn
Introduction to minimum and maximum pointsWorked example: absolute and relative extrema

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

Learn
Increasing, decreasing, positive or negative intervalsWorked example: positive & negative intervals

## Interpreting features of graphs

Learn
Graph interpretation word problem: temperatureGraph interpretation word problem: basketball

## Average rate of change

Learn
Introduction to average rate of changeWorked example: average rate of change from graphWorked example: average rate of change from tableWorked example: average rate of change from equation

## Average rate of change word problems

Learn
Average rate of change word problem: tableAverage rate of change word problem: graphAverage rate of change word problem: equationAverage rate of change review

## Combining functions

Learn
Intro to combining functionsAdding functionsSubtracting functionsAdding and subtracting functionsMultiplying functionsDividing functionsMultiplying and dividing functions

## Composing functions (Algebra 2 level)

Learn
Intro to composing functionsIntro to composing functionsComposing functionsEvaluating composite functionsEvaluating composite functions: using tablesEvaluating composite functions: using graphsFinding composite functionsEvaluating composite functions (advanced)

## Shifting functions

Learn
Shifting functions examplesGraphing shifted functions
Practice
4 questions

## Stretching functions

Learn
Identifying function transformationsIdentifying horizontal squash from graphReflecting & compressing functions

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

Learn
Modeling with function combinationModeling with composite functionsModeling with composite functions (example 2)

## Introduction to inverses of functions (Algebra 2 level)

Learn
Intro to inverse functionsIntro to inverse functionsInputs & outputs of inverse functionsGraphing the inverse of a linear function
Practice

## Finding inverse functions (Algebra 2 level)

Learn
Finding inverse functions: linearFinding inverse functions: quadraticFinding inverse functions: quadratic (example 2)Finding inverse functions: radicalFinding inverses of rational functionsFinding inverse functions

## Verifying that functions are inverses (Algebra 2 level)

Learn
Verifying inverse functions by compositionVerifying inverse functions by compositionVerifying inverse functions by composition: not inverse
Practice

## Determining whether a function is invertible (Algebra 2 level)

Learn
Determining if a function is invertibleIntro to invertible functionsRestricting domains of functions to make them invertible

Learn

Learn
Practice

## Graphing nonlinear piecewise functions (Algebra 2 level)

Learn
Graphs of nonlinear piecewise functions

## Interpreting the symmetry of algebraic models (Algebra 2 level)

Learn
Symmetry of algebraic modelsSymmetry of algebraic models

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

Learn
End behavior of algebraic models

## Interpreting the periodicity of algebraic models (Algebra 2 level)

Learn
Periodicity of algebraic models

## Comparing features of functions (Algebra 2 level)

Learn
Comparing functions: x-interceptsComparing functions: shared featuresComparing maximum points of quadratic functions

## Two-variable functions

Learn
New operator definitions 1New operator definitions 2

#### Unit test

Test your understanding of Functions with these 39 questions.