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Lesson Plans (1) A detailed description of the instruction for teaching one or more concepts or skills. Classroom Resources (1)


ALEX Lesson Plans  
   View Standards     Standard(s): [MA2015] PRE (9-12) 22 :
22 ) (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. [F-BF4c]

Subject: Mathematics (9 - 12)
Title: Building Functions:  Inverse Functions from Tables and Graphs
Description:

This lesson will lead students on a guided discovery to find the inverse of a function given the graph or a table of values. Students will relate the inverse of a graph to finding the reflection of the graph over the line y=x. They will identify characteristics of functions whose inverses are also functions (One-to-One Functions) and will be introduced to the horizontal line test. Students will also apply their knowledge of a graph to a table of values to determine if the table represents a One-to-One Function.

This lesson results from the ALEX Resource Gap Project.




ALEX Classroom Resources  
   View Standards     Standard(s): [MA2015] AL2 (9-12) 35 :
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.

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

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

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

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

[MA2015] ALT (9-12) 35 :
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.

Subject: Mathematics (9 - 12)
Title: Precalculus and Advanced Topics, Module 3: Inverse Functions
URL: https://www.engageny.org/resource/precalculus-and-advanced-topics-module-3-topic-c-overview
Description:

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.



ALEX Classroom Resources: 1

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