For the given function, find all asymptotes of the type indicated (if there are any)
-$f ( x ) = \frac { ( x - 5 ) ( x + 4 ) } { x ^ { 2 } - 9 }$, vertical
A) None
B) $x = 5 , x = - 4$
C) $x = - 5 , x = 4$
D) $x = 3 , x = - 3$

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero (and the numerator is not zero at those points). For $f(x) = \frac{(x - 5)(x + 4)}{x^2 - 9}$, the denominator is $x^2 - 9 = (x - 3)(x + 3)$, which is zero at $x = 3$ and $x = -3$. These are the points where the function is undefined and has vertical asymptotes.

For the Given Function, Find All Asymptotes of the Type f(x)=(x−5)(x+4)x2−9f ( x ) = \frac { ( x - 5 ) ( x + 4 ) } { x ^ { 2 } - 9 }f(x)=x2−9(x−5)(x+4)​

For the Given Function, Find All Asymptotes of the Type $f ( x ) = \frac { ( x - 5 ) ( x + 4 ) } { x ^ { 2 } - 9 }$