Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 3 } { x ^ { 2 } - 9 }$
A) $x = - 3$
B) $x = 3$
C) $x = 0$
D) $x = - 9$
E) $x = 9$

Question

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 3 } { x ^ { 2 } - 9 }$ 
A) $x = - 3$
B) $x = 3$
C) $x = 0$
D) $x = - 9$
E) $x = 9$

Quizplus · Accepted Answer

The denominator $x^2 - 9$ can be factored as $(x + 3)(x - 3)$. Vertical asymptotes occur where the denominator is zero but the numerator is not zero at the same points. Setting $x^2 - 9 = 0$ gives $x = \pm 3$. However, $x = 3$ also makes the numerator zero, which means it's a hole, not an asymptote. Thus, the only vertical asymptote is at $x = -3$.

Find Vertical Asymptotes of the Following Function g(x)=x−3x2−9g ( x ) = \frac { x - 3 } { x ^ { 2 } - 9 }g(x)=x2−9x−3​

Find Vertical Asymptotes of the Following Function $g ( x ) = \frac { x - 3 } { x ^ { 2 } - 9 }$