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 numerator and denominator. The condition $x \neq -5$ is necessary because the original function is undefined at $x = -5$, which is also the location of the vertical asymptote. However, since the $(x + 5)$ term is canceled out, there are actually no vertical asymptotes in the simplified function, but the restriction $x \neq -5$ remains due to the original domain of the function.

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