Find the vertical asymptotes of the rational function.
-$$f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }$$
A) $x = 16 , x = - 2$
B) $x = 0 , x = 16$
C) $x = - 4 , x = 4$
D) $x = - 4 , x = 4 , x = - 2$

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator is zero and the numerator is not zero at those points. Factoring the denominator $x^2 - 16 = (x - 4)(x + 4)$, we find the zeros at $x = 4$ and $x = -4$. These are the points where the function is undefined, leading to vertical asymptotes.

Find the Vertical Asymptotes of the Rational Function f(x)=x+2x2−16f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }f(x)=x2−16x+2​

Find the Vertical Asymptotes of the Rational Function $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }$