# EQUATION OF VERTICAL ASYMPTOTE WORKSHEET

Describe the vertical asymptotes and holes for the graph of each rational function.

Problem 1 :

y = (x - 2)/(x + 2) (x - 2)

Problem 2 :

y = x/x(x - 1)

Problem 3 :

y = (5 - x)/(x2 - 1)

Problem 4 :

y = (x2 - 2)/(x + 2)

Problem 5 :

y = (x2 - 4)/(x2 + 4)

Problem 6 :

y = (x + 3)/(x2 - 9)

Problem 7 :

y = (x2 - 25)/(x – 4)

Problem 8 :

y = (x - 2) (2x + 3)/(5x + 4) (x – 3)

Problem 9 :

y = (15x2 - 7x - 2)/(x2 - 4)

Solution

1)  Vertical asymptote at x = -2; hole at x = 2

2)  Vertical asymptote at x = 1; hole at x = 0

3)  Vertical asymptotes at x = 1 and x = -1

4)  Vertical asymptote at x = -2

5)  No vertical asymptotes and no holes

6)  Vertical asymptote at x = 3; hole at x = -3

7)  Vertical asymptote at x = 4

8)  Vertical asymptotes at x = -4/5 and x = 3.

9)  Vertical asymptotes at x = 2 and x = -2.

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