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 of a fraction equals zero but the numerator does not equal zero at those points. For $g(x) = \frac{x - 5}{x^2 - 25}$, the denominator $x^2 - 25$ factors to $(x + 5)(x - 5)$. Setting this equal to zero gives $x = -5$ and $x = 5$. However, at $x = 5$, the numerator also equals zero, which means it's a hole, not an asymptote. Thus, the only vertical asymptote is at $x = -5$.

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 $g ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$