For the given function, find all asymptotes of the type indicated (if there are any)
-$f ( x ) = \frac { x - 1 } { x ^ { 2 } + 8 }$, vertical
A) $x = 1 , x = - 1$
B) None
C) $x = 8$
D) $x = - 8$

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is equal to zero, as long as the numerator is not also zero at those points. For the given function $f(x) = \frac{x - 1}{x^2 + 8}$, the denominator $x^2 + 8$ is never zero for any real value of $x$ because $x^2$ is always non-negative, making $x^2 + 8$ always positive. Therefore, there are no vertical asymptotes.

For the Given Function, Find All Asymptotes of the Type f(x)=x−1x2+8f ( x ) = \frac { x - 1 } { x ^ { 2 } + 8 }f(x)=x2+8x−1​

For the Given Function, Find All Asymptotes of the Type $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 8 }$