Asymptotes of Rational Functions 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)

Solution

Problem 3 :

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

Solution

Problem 4 :

y = (2x² + 3)/(x² – 6)

Solution

Problem 5 :

y = (3x - 12)/(x² – 2)

Solution

Problem 6 :

y = (3x³ – 4x + 2)/(2x³ + 3)

Solution

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

Problem 1 :

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

Solution

Problem 2 :

y = x/x(x - 1)

Solution

Problem 3 :

y = (5 - x)/(x² - 1)

Solution

Problem 4 :

y = (x² - 2)/(x + 2)

Solution

Problem 5 :

y = (x² - 4)/(x² + 4)

Solution

Problem 6 :

y = (x + 3)/(x² - 9)

Solution

Problem 7 :

y = (x² - 25)/(x – 4)

Solution

Problem 8 :

y = (x - 2) (2x + 3)/(5x + 4) (x – 3)

Solution

Problem 9 :

y = (15x² - 7x - 2)/(x² - 4)

Solution

Find the oblique asymptote of the rational functions.

Problem 1 :

f(x) = (x² + 8x – 20)/(x – 1)

Solution

Problem 2 :

f(x) = (6x³ – 1)/(-2x² + 18)

Solution

Problem 3 :

f(x) = (2x² + x – 5)/(x + 1)

Solution

Problem 4 :

f(x) = (2x² - 5x + 3)/(x – 1)

Solution

Problem 5 :

f(x) = (2x² - 5x + 5)/(x – 2)

Solution

Problem 6 :

f(x) = (x³ - 2x² + 5)/x²

Solution

Problem 7 :

f(x) = (x³ - x² - x - 1)/(x – 3) (x + 4)

Solution

Problem 8 :

f(x) = x³/(x² – 4)

Solution