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What is a function?Worked example: Evaluating functions from equationWorked example: Evaluating functions from graphWorked example: evaluating expressions with function notation
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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)
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Equations vs. functionsObtaining a function from an equation
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Function notation word problem: bankFunction notation word problem: beach
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Intervals and interval notationWhat is the domain of a function?What is the range of a function?Worked example: domain and range from graph
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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)
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Recognizing functions from graphDoes a vertical line represent a function?Recognizing functions from tableRecognizing functions from verbal descriptionRecognizing functions from verbal description word problem
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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
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Introduction to minimum and maximum pointsWorked example: absolute and relative extrema
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Increasing, decreasing, positive or negative intervalsWorked example: positive & negative intervals
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Graph interpretation word problem: temperatureGraph interpretation word problem: basketball
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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
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Average rate of change word problem: tableAverage rate of change word problem: graphAverage rate of change word problem: equationAverage rate of change review
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Intro to combining functionsAdding functionsSubtracting functionsAdding and subtracting functionsMultiplying functionsDividing functionsMultiplying and dividing functions
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Intro to composing functionsIntro to composing functionsComposing functionsEvaluating composite functionsEvaluating composite functions: using tablesEvaluating composite functions: using graphsFinding composite functionsEvaluating composite functions (advanced)
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Shifting functions examplesGraphing shifted functions
Practice
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Identifying function transformationsIdentifying horizontal squash from graphReflecting & compressing functions
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Modeling with function combinationModeling with composite functionsModeling with composite functions (example 2)
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Intro to inverse functionsIntro to inverse functionsInputs & outputs of inverse functionsGraphing the inverse of a linear function
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Finding inverse functions: linearFinding inverse functions: quadraticFinding inverse functions: quadratic (example 2)Finding inverse functions: radicalFinding inverses of rational functionsFinding inverse functions
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Verifying inverse functions by compositionVerifying inverse functions by compositionVerifying inverse functions by composition: not inverse
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Determining if a function is invertibleIntro to invertible functionsRestricting domains of functions to make them invertible
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Domain and range of quadratic functionsRange of quadratic functions
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Symmetry of algebraic modelsSymmetry of algebraic models
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Comparing functions: x-interceptsComparing functions: shared featuresComparing maximum points of quadratic functions
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New operator definitions 1New operator definitions 2
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