Module 7: Rational Functions and Function Operations

 

In Try This 3 you may have noticed that an x-intercept occurs when a factor that only occurs in the numerator is equal to 0. This is because this makes the entire numerator 0, and, therefore, the function 0.

 

This diagram shows an x-intercept on a rational function. It is labelled “x-intercepts occur when a factor only in the numerator is equal to 0.”



textbook

Read “Example 3” on pages 449 and 450 of the textbook. Pay attention to how asymptotes, points of discontinuity, and x-intercepts are used to help match the equations to their graphs.

 

 

Self-Check 2
  1. Add another column to the summary table you saw just after Try This 2. The first row of your table will look like this:

      When a factor that occurs in both the numerator and denominator is equal to 0 When a factor that occurs only in the denominator is equal to 0 When a factor that occurs only in the numerator is equal to 0
    Function

    Functions will vary. An example is provided.

     

    Complete the last column to describe what happens if there is a factor that occurs only in the numerator. Answer

 

textbook

  1. Complete “Your Turn” from “Example 3” on page 450 of the textbook. Answer
  2. Complete questions 4, 5, 8.a., 8.b., and 11 on pages 452 and 453 of the textbook. Answer

glossary
Add the following terms to your copy of Glossary Terms: