ALEX Classroom Resource

  

Precalculus and Advanced Topics, Module 3: Inverse Functions

  Classroom Resource Information  

Title:

Precalculus and Advanced Topics, Module 3: Inverse Functions

URL:

https://www.engageny.org/resource/precalculus-and-advanced-topics-module-3-topic-c-overview

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 3, Topic C students study inverse functions, being careful to understand when inverse functions do and do not exist, working to restrict the domain of a function to produce an invertible function. They compare and create different representations of functions including tables and graphs. Students compose functions to verify that one function is the inverse of another and work with tables of data to identify features of inverse functions. Special emphasis is given to the inverse relationship between exponential and logarithmic functions.

Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Algebra II and Algebra II with Trigonometry Alabama Courses of Study.

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II
35 ) Find inverse functions. [F-BF4]

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. [F-BF4a]

Example: f(x) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.

Mathematics
MA2015 (2016)
Grade: 9-12
Precalculus
21 ) (+) Verify by composition that one function is the inverse of another. [F-BF4b]

Mathematics
MA2015 (2016)
Grade: 9-12
Precalculus
22 ) (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. [F-BF4c]

Mathematics
MA2015 (2016)
Grade: 9-12
Precalculus
23 ) (+) Produce an invertible function from a non-invertible function by restricting the domain. [F-BF4d]

Mathematics
MA2015 (2016)
Grade: 9-12
Precalculus
24 ) (+) Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. [F-BF5]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II with Trigonometry
35 ) Find inverse functions. [F-BF4]

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. [F-BF4a]

Example f(x) = 2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.

Tags: domain, exponents, graph, inverse functions, inverse relationship, invertible function, logarithms, table
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Comments

There are four lessons on this topic.

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site. 

Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Algebra II and Algebra II with Trigonometry Alabama Courses of Study.

  This resource provided by:  
Author: Hannah Bradley