11. Modeling with Functions

11.01 Review: Relations and functions

11.02 Function families and transformations

11.03 Choosing appropriate models

11.04 Domain and range and continuity

11.05 Characteristics from a graph

11.06 Average rates of change

11.07 Comparing function types

11.08 Solutions from a graph

11.09 Operations with functions

11.10 Inverse relations and functions

11.11 Applications of quadratic functions

Investigation: Sine waves and music

Investigation: Modeling tsunami movement

11.12 Fitting functions to quadratic data

United States of America UT

Math III

11.10 Inverse relations and functions

Interactive practice questions

Consider the graph of each function below and determine if it has an inverse function.

a

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A graph of cubic function with only one x-intercept on a coordinate plane.

Has an inverse function.

A

Does not have an inverse function.

B

b

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A graph of cubic function with three x-intercept on a coordinate plane.

Has an inverse function.

A

Does not have an inverse function.

B

Easy

< 1min

For each function graphed below, determine if it has an inverse function.

Easy

< 1min

Do the following graphs have inverse functions?

Easy

< 1min

Outcomes

III.F.BF.4.a

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. Include linear, quadratic, exponential, logarithmic, rational, square root, and cube root functions.

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