Simplify $f$ below and find any vertical asymptotes of $f$.
$$f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$$
A) $f ( x ) = x + 5 , x \neq 5$; vertical asymptotes: none
B) $f ( x ) = x - 5 , x \neq - 5$; vertical asymptotes: none
C) $f ( x ) = x - 5 , x \neq 5$; vertical asymptotes: none
D) $f ( x ) = x + 5 , x \neq - 5$; vertical asymptotes: $x = - 5$
E) $f ( x ) = x - 5 , x \neq 5$; vertical asymptotes: $x = 5$

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{x^2 - 25}{x + 5}$ simplifies to $f(x) = x - 5$ when factoring the numerator as $(x - 5)(x + 5)$ and canceling out the $(x + 5)$ term in the denominator. However, $x \neq -5$ because the original function is undefined at $x = -5$, which is also where the vertical asymptote is located. The correct choice does not mention the vertical asymptote, which is an oversight in the question's options.

Simplify fff Below and Find Any Vertical Asymptotes Of fff f(x)=x2−25x+5f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }f(x)=x+5x2−25​

Simplify $f$ Below and Find Any Vertical Asymptotes Of $f$ $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$