Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give
the equation of the asymptote if it exists.
-$f ( x ) = \frac { x ^ { 3 } + 3 } { x ^ { 2 } + 8 x }$
A)Oblique asymptote: y = x - 8
B)Horizontal asymptote: y = 1
C)Neither

Question

Quizplus · Accepted Answer

To determine the type of asymptote, compare the degrees of the numerator and denominator. Here, the numerator is degree 3 and the denominator is degree 2. When the degree of the numerator is exactly one more than the degree of the denominator, the graph has an oblique asymptote. To find the equation of the oblique asymptote, perform polynomial long division or synthetic division of the numerator by the denominator. The quotient (ignoring the remainder) gives the equation of the oblique asymptote, which is $y = x - 8$.

Determine Whether the Graph of the Rational Function Has a Horizontal