FINDING HOLES AND VERTICAL ASYMPTOTES WORKSHEET
Describe the vertical asymptotes and holes for the graph of each rational function.
Problem 1 :
Problem 2 :
Problem 3 :
Problem 4 :
Problem 5 :
Problem 6 :
Problem 7 :
Problem 8 :
Problem 9 :
Problem 10 :
Suppose you start a home business typing technical research papers for college students. You must spend $3500 to replace your computer system. Then you estimate the cost of typing each page will be $0.02.
a. Write a rational function modeling your average cost per page. Graph the function.
b. How many pages must you type to bring your average cost per page to less than $1.50 per page, the amount you plan to charge?
Answer Key
1) Vertical asymptotes are x = -2 and x = 2.
There is a hole at x = 2.
2) Vertical asymptotes are x = 0 and x = 1.
There is a hole at x = 0.
3) Vertical asymptotes are x = 1 and x = -1.
There is no hole for the given rational function
4) vertical asymptote is x = -2.
There is no hole for the given rational function.
5) There is no asymptote.
There is no hole for the given rational function.
6) vertical asymptotes are x = -3 and x = 3.
There is a hole at x = -3.
7) Vertical asymptote is x = 4.
there is no hole for the given rational function.
8) vertical asymptotes are x = -4/5 and x = 3.
there is no hole for the given rational function.
9) the vertical asymptotes are x = 2 and x = -2.
there is no hole for the given rational function.
10) a)
b. Average cost should be less than 1.50.
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