Question

find the vertical asymptotes of the graph of the rational function.
$y = \frac{x - 5}{x + 16}$

the equation(s) of the vertical asymptote(s) is/are $x = \square$.
(use a comma to separate answers as needed.)

Explanation:

Step1: Recall the rule for vertical asymptotes of rational functions

For a rational function \( y = \frac{f(x)}{g(x)} \), vertical asymptotes occur where the denominator \( g(x) = 0 \) (provided the numerator \( f(x)
eq 0 \) at those points).

Step2: Set the denominator equal to zero and solve for \( x \)

For the function \( y=\frac{x - 5}{x + 16} \), the denominator is \( x + 16 \). We set \( x+16 = 0 \).
Solving the equation \( x+16=0 \), we subtract 16 from both sides: \( x=- 16 \).
We also check the numerator at \( x = - 16 \): \( f(-16)=-16 - 5=-21
eq0 \), so \( x=-16 \) is a vertical asymptote.

Answer:

\(-16\)