Questions on Rational Functions

What's On This Page

This page contains sample problems on rational functions. They are for Self-assessment and Review.

Each problem (or group of problems) has an "answer button" ANSWER which you can click to look at an answer. Some solutions have a "further explanation button" Explain which you can click to see a more complete, detailed solution.

What to Do

To gain the most benefit from these problems,

Work the problems on your own. Write down your solutions BEFORE looking at any answers.

Use a graphing calculator as appropriate. A graphing calculator can be used to verify that your answers "make sense" or "look right".

If you have difficulties with this material, please contact your instructor. (See Getting Help in Stage 1.) Rational functions and their graphs are used throughout CalculusQuestTM. If you have trouble with the basics of rational functions, this trouble will not go away.

1. Find the domain and any zeros, vertical asymptotes, horizontal asymptotes and holes for the following rational functions. The functions may exhibit all, some or none of the above features.

  1. x - 4
    g(x) = --------------
    2x + 1

  2. x
    f(x) = --------------
    x2 + 3

  3. x + 1
    r(x) = ------------------
    x2 - 3 x - 4

  4. x2 - 9
    h(x) = --------------
    x + 5


2. Scott and Ian design a cool T-shirt for snow boarders. Their friends are very impressed and everybody wants one, so Scott and Ian set up a T-shirt printing business in their garage. Total start-up costs are $450 due to the availability of a used graphics machine. They estimate that it costs them $5.50 to print each T-shirt.

  1. Write a linear function C(x) giving the total cost of producing x T-shirts. Remember to take the start-up cost into account.

  2. Write a rational function A(x) giving the average cost of producing x T-shirts.

  3. What is the domain of A(x) in the context of the problem? Explain.

  4. Does A(x) have a vertical asymptote? If so what is its equation?

  5. Find the horizontal asymptote for A(x). What meaning does this value have in the context of the problem?


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