Find the vertical asymptotes of the rational function.
-$$f ( x ) = \frac { x - 4 } { 16 x - x ^ { 3 } }$$
A) $x = 0 , x = 4$
B) $x = 0 , x = - 4$
C) $x = - 4 , x = 4$
D) $x = 0 , x = - 4 , x = 4$

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator is zero and the numerator is not zero at those points. Factoring the denominator gives $16x - x^3 = x(16 - x^2) = x(4 - x)(4 + x)$. Setting this equal to zero gives $x = 0$, $x = 4$, and $x = -4$. However, $x = 4$ is not a vertical asymptote because it makes the numerator zero as well, leaving $x = 0$ and $x = -4$ as the correct answers.

Find the Vertical Asymptotes of the Rational Function f(x)=x−416x−x3f ( x ) = \frac { x - 4 } { 16 x - x ^ { 3 } }f(x)=16x−x3x−4​

Find the Vertical Asymptotes of the Rational Function $f ( x ) = \frac { x - 4 } { 16 x - x ^ { 3 } }$