# FINDING EQUATION OF HORIZONTAL ASYMPTOTES WORKSHEET

Find the horizontal asymptote of the graph of each rational function.

Problem 1 :

y = 2/(x – 6)

Solution

Problem 2 :

y = (x + 2)/(x – 4)

Problem 3 :

y = (x + 3)/2(x + 4)

Problem 4 :

y = (2x2 + 3)/(x2 – 6)

Problem 5 :

y = (3x - 12)/(x2 – 2)

Problem 6 :

y = (3x– 4x + 2)/(2x3 + 3)

1)  y = 0

2)  y = 1

3)  y = 1/2

4)  y = 2

5)  y = 0 which is the x – axis.

6)  y = 1.5.

Find the oblique asymptote of the rational functions.

Problem 1 :

f(x) = (x2 + 8x – 20)/(x – 1)

Problem 2 :

f(x) = (6x3 – 1)/(-2x2 + 18)

Problem 3 :

f(x) = (2x2 + x – 5)/(x + 1)

Problem 4 :

f(x) = (2x2 - 5x + 3)/(x – 1)

Problem 5 :

f(x) = (2x2 - 5x + 5)/(x – 2)

Problem 6 :

f(x) = (x3 - 2x2 + 5)/x2

Problem 7 :

f(x) = (x3 - x- x - 1)/(x – 3) (x + 4)

Problem 8 :

f(x) = x3/(x2 – 4)

Solution

1)  y = x + 9

2)  y = -3x

3)  y = 2x - 1

4)  y = 2x + 3

5)  y = 2x + 1

6)  y = x + 2

7)  y = x – 2

8) Vertical asymptotes at x = -2 and 2

Oblique asymptote is at y = x-4

x-intercept is at x = 0

y-intercept is at x = 0

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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