1. Lesson 5

Mathematics 30-1 Module 1

Module 1: Function Transformations

 

Lesson 5: Inverse of a Relation

 
Focus

 

The series of photos show a regular face, a face with the bottom narrowed, the photo split into strips, a painted effect added, and then a ripple effect added.

Polka Dot/Thinkstock

Various photo manipulation programs are available that can make editing photos simple and fun. Look at the top sequence of photos and determine the change between each step. Now look at the second series of photos, which was manipulated in the same manner. Suppose you wanted to determine what the original photo looked like. What steps would you have to take? Would the order of these steps be important?



This is a different face with similar distortions to the final picture in the last sequence.

Hemera Technologies/PhotoObjects.net/Thinkstock

Recall that a function is a rule that associates an input with an output. Just as the steps used to modify a photograph can be reversed to determine the original, the instructions given by a function can be reversed—you can use the output of a function to determine the input. The ability to reverse a process is important in many areas of mathematics, and this ability is a key idea in algebra. In Lesson 5 you will investigate how to reverse the output from a function.

Lesson Outcomes

 

At the end of this lesson you will be able to

  • determine the graph of the inverse of f(x) given the graph of f(x)
  • determine the equation of the inverse of f(x) given the equation of f(x)
Lesson Question

 

You will investigate the following question:

  • How are a function and its inverse related?
Assessment

 

Your assessment may be based on a combination of the following tasks:

  • completion of the Lesson 5 Assignment (Download the Lesson 5 Assignment and save it in your course folder now.)
  • course folder submissions from Try This, and Share activities
  • additions to Glossary Terms
  • work under Project Connection
Materials and Equipment
  • graph paper