Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 6 } { x ^ { 2 } - 36 }$
A) $x = 36$
B) $x = - 6$
C) $x = - 36$
D) $x = 6$
E) $x = 0$

Question

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 6 } { x ^ { 2 } - 36 }$ 
A) $x = 36$
B) $x = - 6$
C) $x = - 36$
D) $x = 6$
E) $x = 0$

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a fraction equals zero but the numerator does not equal zero at those points. For $g(x) = \frac{x - 6}{x^2 - 36}$, the denominator is $x^2 - 36$, which factors to $(x + 6)(x - 6)$. Setting this equal to zero gives $x = -6$ and $x = 6$. However, $x = 6$ also makes the numerator zero, which means it's not a vertical asymptote but a point where the function is undefined. Therefore, the only vertical asymptote is at $x = -6$.

Find Vertical Asymptotes of the Following Function g(x)=x−6x2−36g ( x ) = \frac { x - 6 } { x ^ { 2 } - 36 }g(x)=x2−36x−6​

Find Vertical Asymptotes of the Following Function $g ( x ) = \frac { x - 6 } { x ^ { 2 } - 36 }$