B Apply

Find the vertical and horizontal asymptotes, if any, of the graph of each rational function.

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39. Think About a Plan A basketball player has made 21 of her last 30 free throws—a percentage of 70%. How many more consecutive free throws does she need to raise her free throw percentage to 75%?
    • How can you model the player's free throw percentage as a rational function? (Hint: Let x = x equals  the number of additional free throws needed.)
    • How can a graph help you answer this question?
40. Grades A student earns an 82% on her first test. How many consecutive 100% test scores does she need to bring her average up to 95%? Assume that each test has equal impact on the average grade.

41. Error Analysis A student listed the asymptotes of the function y = x 2 − 3 x + 2 x 2 + 6 x + 5 y equals . fraction x squared , minus 3 x plus 2 , over x squared , plus 6 x plus 5 end fraction  as shown below. Explain the student's error. What are the correct asymptotes?

    

Sketch the graph of each rational function.

42. y = 2 x + 3 x − 5 y equals . fraction 2 x plus 3 , over x minus 5 end fraction
43. y = x 2 + 6 x + 9 x + 3 y equals . fraction x squared , plus 6 x plus 9 , over x plus 3 end fraction
44. y = 4 x 2 − 100 2 x 2 + x − 15 y equals . fraction 4 , x squared , minus 100 , over 2 , x squared , plus x minus 15 end fraction
45. y = − x ( x − 1 ) 2 y equals negative . fraction x , over open , x minus 1 , close squared end fraction
46. Business CDs can be manufactured for $.19 each. The development cost is $210,000. The first 500 discs are samples and will not be sold.
    1. Write a function for the average cost of a disc that is not a sample. Graph the function.
    2. What is the average cost if 5000 discs are produced? If 15,000 discs are produced?
    3. How many discs must be produced to bring the average cost under $10?
    4. What are the vertical and horizontal asymptotes of the graph of the function?
47. Writing Describe the conditions that will produce a rational function with a graph that has no vertical asymptotes.

C Challenge

48. Reasoning Look for a pattern in the sequence of file folders below.
    1. Write a model for the number of yellow folders Y(n) at each step n.
    2. Write a model for the number of green folders G(n) at each step n.

    3. Write a model for the ratio of Y(n) to G(n). Use it to predict the ratio of yellow folders to green folders in the next figure. Verify your answer.

       
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