Question

6.9.3 quiz: finding vertical asymptotes
question 1 of 10
at what value of x does the graph of the following function f(x) have a vertical asymptote?
f(x)=\frac{1}{x + 1}
a. 0
b. 1
c. 2
d. -1

Explanation:

Step1: Recall the condition for vertical asymptote

For a rational function \(F(x)=\frac{f(x)}{g(x)}\), vertical asymptotes occur at the values of \(x\) that make the denominator \(g(x) = 0\) (assuming the numerator \(f(x)
eq0\) at those values).

Step2: Set the denominator equal to zero

Given \(F(x)=\frac{1}{x + 1}\), set the denominator \(x+1=0\).

Step3: Solve for \(x\)

Subtract \(1\) from both sides of the equation \(x+1 = 0\). We get \(x=-1\).

Answer:

D. -1