Inverse Functions

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Objective

SWBAT explain what an inverse function is and determine the inverse function given a one-to-one function.

Big Idea

A function performs a series of operations on the input to produce and output; an inverse function undoes all of these operations in the reverse order they were performed.

Warm-Up

20 minutes

Mini-Lesson: Inverse Functions

20 minutes

Building on the warm-up activity and the Inverse Functions powerpoint presentation from the previous day's lesson, I write out the following notes on the board:

  1. A step-by-step process for finding the inverse of a function presented algebraically
  2. A process for finding the inverse of a function presented graphically
  3. A process for finding the inverse of a function presented numerically

In all my instruction about inverse functions, I emphasize that inverse functions are all about switching the domain and range of a function.  I hope that remembering this big picture concept will help the work with inverse function feel less abstract and more manageable.

Group Work

40 minutes

To practice the skills outlined in the notes, students work in groups to complete WS Inverse Functions.   This is a collection of problems that promote flexibility in working with inverse functions. Students convert between algebraic, numeric, and graphical representations of inverse functions.

Assignment

10 minutes

To solidify their understanding of inverse functions and how to represent them, students complete Inverse Function Homework for the night's assignment.  I anticipate that this assignment will take my students about 30 minutes.  I provide an answer key through Edmodo so that they can check their answers before coming to class.