Question

use the denominator to identify all places where the functions below are discontinuous. then check the value of the numerator at each discontinuity to determine if each discontinuity is a removable discontinuity (\hole\) or an infinite discontinuity (vertical asymptote). 1. $y = \frac{1}{x + 5}$

Explanation:

Step1: Find the discontinuity

Set the denominator equal to zero: $x + 5=0$.
Solve for $x$: $x=-5$.

Step2: Check the numerator at the discontinuity

The numerator is $1$. When $x = - 5$, the numerator is still $1
eq0$.

Answer:

The function $y=\frac{1}{x + 5}$ is discontinuous at $x=-5$. Since the numerator is non - zero at $x=-5$, there is an infinite discontinuity (vertical asymptote) at $x=-5$.