Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
-$f ( x ) = \frac { x ^ { 2 } - 4 x - 5 } { x + 1 }$
A)-1: hole
B)1: hole
C)1: vertical asymptote
D)-1: vertical asymptote

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{x^2 - 4x - 5}{x + 1}$ can be simplified by factoring the numerator as $(x-5)(x+1)$. This simplifies to $f(x) = x - 5$ when $x \neq -1$, indicating a hole at $x = -1$, since the factor $x + 1$ cancels out, leaving the function defined everywhere except at $x = -1$.

Find All Points of Discontinuity, and Determine Whether There Is f(x)=x2−4x−5x+1f ( x ) = \frac { x ^ { 2 } - 4 x - 5 } { x + 1 }f(x)=x+1x2−4x−5​

Find All Points of Discontinuity, and Determine Whether There Is $f ( x ) = \frac { x ^ { 2 } - 4 x - 5 } { x + 1 }$