Module 1: Function Transformations

 

The following example describes how to determine the inverse of a function, the domain and range of both relations, and whether the inverse is a function.



textbook

Read “Link the Ideas” and “Example 1” on pages 46 and 47 of the textbook.

 

 

In “Example 1” you saw that the inverse of a function may not be a function. When this is the case, function notation is not appropriate—that is, y = f −1(x) may not be an appropriate title for the inverse. In this case, the title “inverse of f(x)” may be used.

 

Just as you can check if a relation is a function by using the vertical line test, a horizontal line test can be used to determine if the inverse of a relation is a function. If it is possible for a horizontal line to cross the graph of a relation at more than one point, the inverse will not be a function.

 

The diagram shows a function passing through (–2, 2), (–1, –2), and (1, 1). A horizontal line passes through the function at two points.

 

Self-Check 1

 

textbook

  1. Complete “Your Turn” from “Example 1” on page 47 of the textbook. Answer
  2. Complete “Check Your Understanding” question 2 on page 51 of the textbook. Answer

Although the inverse of a function may not be a function, it is often possible to restrict the domain of the function so the inverse is a function. The following example explains how.



textbook

Read “Example 2” on page 48 of your textbook.

 

 

 

Self-Check 2
  1. Complete “Your Turn” for “Example 2” on page 48 of the textbook. Answer
  2. Complete “Check Your Understanding” questions 4.a. and 4.d. on page 52 of the textbook. Answer