Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
-$g ( x ) = \frac { x } { x + 5 }$
A)-5: vertical asymptote
B)0: vertical asymptote; 5: vertical asymptote
C)0: vertical asymptote; -5: vertical asymptote
D)no vertical asymptotes

Question

Quizplus · Accepted Answer

The function $g(x) = \frac{x}{x+5}$ has a point of discontinuity at $x = -5$ because the denominator becomes zero, making the function undefined at this point. This results in a vertical asymptote at $x = -5$, not a hole, because the numerator does not also become zero at $x = -5$. There are no other points of discontinuity, as the function is defined for all other real numbers.

Find All Points of Discontinuity, and Determine Whether There Is g(x)=xx+5g ( x ) = \frac { x } { x + 5 }g(x)=x+5x​

Find All Points of Discontinuity, and Determine Whether There Is $g ( x ) = \frac { x } { x + 5 }$