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Functions

Evaluating functions

Learn
What is a function?
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Worked example: Evaluating functions from equation
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Worked example: Evaluating functions from graph
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Evaluating discrete functions
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Worked example: evaluating expressions with function notation
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Practice
Evaluate functionsGet 3 of 4 questions to level up!
Evaluate functions from their graphGet 3 of 4 questions to level up!
Evaluate function expressionsGet 3 of 4 questions to level up!

Inputs and outputs of a function

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Worked example: matching an input to a function's output (equation)
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Worked example: matching an input to a function's output (graph)
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Worked example: two inputs with the same output (graph)
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Practice
Function inputs & outputs: equationGet 3 of 4 questions to level up!
Function inputs & outputs: graphGet 3 of 4 questions to level up!

Functions and equations

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Equations vs. functions
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Obtaining a function from an equation
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Practice
Function rules from equationsGet 3 of 4 questions to level up!

Interpreting function notation

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Function notation word problem: bank
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Function notation word problem: beach
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Practice
Function notation word problemsGet 3 of 4 questions to level up!

Introduction to the domain and range of a function

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Intervals and interval notation
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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 graphGet 5 of 7 questions to level up!

Determining the domain of a function

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Determining whether values are in domain of function
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Examples finding the domain of functions
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Worked example: determining domain word problem (real numbers)
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Worked example: determining domain word problem (positive integers)
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Worked example: determining domain word problem (all integers)
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Practice
Identifying values in the domainGet 3 of 4 questions to level up!
Determine the domain of functionsGet 3 of 4 questions to level up!
Function domain word problemsGet 3 of 4 questions to level up!

Recognizing functions

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Recognizing functions from graph
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Does a vertical line represent a function?
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Recognizing functions from table
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Recognizing functions from verbal description
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Recognizing functions from verbal description word problem
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Practice
Recognize functions from graphsGet 3 of 4 questions to level up!
Recognize functions from tablesGet 3 of 4 questions to level up!

Maximum and minimum points

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Introduction to minimum and maximum points
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Worked example: absolute and relative extrema
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Practice
Relative maxima and minimaGet 3 of 4 questions to level up!
Absolute maxima and minimaGet 3 of 4 questions to level up!

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

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Increasing, decreasing, positive or negative intervals
(Opens a modal)
Worked example: positive & negative intervals
(Opens a modal)
Practice
Positive and negative intervalsGet 3 of 4 questions to level up!
Increasing and decreasing intervalsGet 3 of 4 questions to level up!

Interpreting features of graphs

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Graph interpretation word problem: temperature
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Graph interpretation word problem: basketball
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Practice
Graph interpretation word problemsGet 3 of 4 questions to level up!

Average rate of change

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Introduction to average rate of change
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Worked example: average rate of change from graph
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Worked example: average rate of change from table
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Practice
Average rate of change: graphs & tablesGet 3 of 4 questions to level up!

Average rate of change word problems

Learn
Average rate of change word problem: table
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Average rate of change word problem: graph
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Average rate of change review
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Practice
Average rate of change word problemsGet 3 of 4 questions to level up!

Intro to inverse functions

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Intro to inverse functions
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Intro to inverse functions
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Inputs & outputs of inverse functions
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Graphing the inverse of a linear function
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Finding inverse functions: linear
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Practice
Evaluate inverse functionsGet 3 of 4 questions to level up!
Finding inverses of linear functionsGet 3 of 4 questions to level up!

About this unit

In this unit, we learn about functions, which are mathematical entities that assign unique outputs to given inputs. We'll evaluate, graph, analyze, and create various types of functions.