Find vertical asymptotes of the following function. $$g ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$$
A)x = 25
B)x = -5
C)x = -25
D)x = 5
E)x = 0

Question

Find vertical asymptotes of the following function.​ $$g ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$$ ​
A)x = 25
B)x = -5
C)x = -25
D)x = 5
E)x = 0

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator is zero and the numerator is not zero at the same point. Factoring the denominator $x^2 - 25 = (x + 5)(x - 5)$, we see that $x = -5$ and $x = 5$ make the denominator zero. However, $x = 5$ also makes the numerator zero, which means it's a hole, not an asymptote. Thus, only $x = -5$ is a vertical asymptote.

Find Vertical Asymptotes of the Following Function g(x)=x−5x2−25g ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }g(x)=x2−25x−5​

Find Vertical Asymptotes of the Following Function $g ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$