Question

determine the vertical asymptote(s) of the following function. if none exists, state that fact.
$f(x) = \frac{x + 4}{x^2 + 9x + 20}$

select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice

a. the function has one vertical asymptote, \boxed{} (type an equation.)

b. the function has three vertical asymptotes. the leftmost asymptote is \boxed{}, the middle asymptote is \boxed{}, and the rightmost asymptote is \boxed{}. (type equations.)

c. the function has two vertical asymptotes. the leftmost asymptote is \boxed{} and the rightmost asymptote is \boxed{}. (type equations.)

d. the function has no vertical asymptotes.

Explanation:

Step1: Factor denominator

Denominator: $x^2 + 9x + 20 = (x+4)(x+5)$
Function becomes: $f(x)=\frac{x+4}{(x+4)(x+5)}$ (simplify if $x
eq-4$)

Step2: Find undefined points

Undefined when denominator=0: $x=-4$ or $x=-5$

Step3: Check for asymptotes

At $x=-4$: numerator=0, so it's a hole (not asymptote).
At $x=-5$: numerator≠0, so it's a vertical asymptote.

Answer:

A. The function has one vertical asymptote, $x=-5$