Find the slant asymptote, if any, of the graph of the rational function.
-$$h ( x ) = \frac { x ^ { 3 } + 8 } { x ^ { 2 } - 9 }$$
A) $y = x$
B) $y = x + 8$
C) $y = x - 9$
D) no slant asymptote

Question

Quizplus · Accepted Answer

To find the slant (oblique) asymptote of the given rational function $h(x) = \frac{x^3 + 8}{x^2 - 9}$, we perform polynomial long division or synthetic division. The slant asymptote is given by the quotient (ignoring the remainder) when the degree of the numerator is exactly one more than the degree of the denominator. Dividing $x^3 + 8$ by $x^2 - 9$, we get a quotient of $x$, which means the slant asymptote is $y = x$.

Find the Slant Asymptote, If Any, of the Graph of the Rational