1. Complete “Your Turn” from “Example 2” on page 449 of the textbook. Answer
2. Complete questions 1, 2.a., 2.b., and 3 on page 451 of the textbook. Answer

So far, you have looked at what happens if a factor occurs in both the numerator and denominator and if a factor occurs just in the denominator of a rational function. In Try This 3 you will look at what happens when a factor is only in the numerator.

Try This 3

Consider the rational function .

1.  
   1. What factor occurs only in the numerator?
   2. What factor occurs only in the denominator?
   3. What factor occurs in both the numerator and denominator?
2. Using the information from question 1, predict where a point of discontinuity and an asymptote will occur on the graph of y = f(x).
3.  
   1. Graph y = f(x) to check your predictions from question 2.
   2. What occurs on the graph when the factor that is only in the numerator is equal to 0?
4.  
   1. Predict whether the event you found in question 3.b. always occurs when a factor is in the numerator but not the denominator.
   2. Explain how you can further test this prediction.
   3. Use your strategy to test your prediction.
5. Use “General Form of a Rational Function” to check your predictions from question 4.
   
   
    
   
   

   Screenshot reprinted with permission of ExploreLearning

   
   
6. Use “General Form of a Rational Function” from question 5 to graph the following functions. State the x-intercepts for each function.
   1. 
   2. 
   3. 
7. How does the prediction you made in question 4 relate to the intercepts you found in question 6?

Save your responses in your course folder.

Share 2

With a partner or group, discuss the following question based on the information from Try This 3:

How can you explain the phenomenon of determining the x-intercept using ideas from earlier in this course or previous courses?

If required, save a record of your discussion in your course folder.