Find the vertical asymptotes, if any, of the graph of the rational function.
-$$g ( x ) = \frac { x } { x ^ { 2 } - 25 }$$
A) $x = 5 , x = - 5$
B) $x = 5 , x = - 5 , x = 0$
C) $x = 5$
D) no vertical asymptote

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero (as long as the numerator is not zero at the same points). For $g(x) = \frac{x}{x^2 - 25}$, the denominator is zero when $x^2 - 25 = 0$, which factors into $(x - 5)(x + 5) = 0$. This gives $x = 5$ and $x = -5$ as the points where the function has vertical asymptotes.

Find the Vertical Asymptotes, If Any, of the Graph of the Rational