Question

for which value of x does the graph of the following function f(x) have a vertical asymptote?
f(x) = \frac{3}{x + 5}

a. -3
b. 5
c. 3
d. -5

Explanation:

Step1: Recall vertical asymptote rule

A rational function \( F(x)=\frac{f(x)}{g(x)} \) has a vertical asymptote where \( g(x) = 0 \) (and \( f(x)
eq0 \) at that point).

Step2: Set denominator to zero

For \( F(x)=\frac{3}{x + 5} \), set the denominator \( x + 5=0 \).

Step3: Solve for x

Solve \( x + 5 = 0 \), we get \( x=-5 \).

Answer:

D. -5