Determine the vertical asymptote(s) of the graph of the function.
-$$f ( x ) = \frac { x } { x ^ { 2 } + 81 }$$
A) $x = 9$ and $x = - 9$
B) $x = 9$ and $x = 0$
C) $x = 9$
D) None

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero, as long as the numerator is not also zero at those points. For the given function $f(x) = \frac{x}{x^2 + 81}$, the denominator $x^2 + 81$ is never zero because $x^2$ is always non-negative, making $x^2 + 81$ always positive. Therefore, there are no vertical asymptotes.

Determine the Vertical Asymptote(s) of the Graph of the Function f(x)=xx2+81f ( x ) = \frac { x } { x ^ { 2 } + 81 }f(x)=x2+81x​

Determine the Vertical Asymptote(s) of the Graph of the Function $f ( x ) = \frac { x } { x ^ { 2 } + 81 }$