Question

find the vertical asymptote(s) of the graph of the function.
g(x)=\frac{1}{(x - 3)^2}
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,
(type an equation.)
○ b. the function has two vertical asymptotes. the leftmost asymptote is and the rightmost asymptote is
(type equations.)
○ c. the function has no vertical asymptotes.

Explanation:

Step1: Recall the definition of vertical asymptote

A vertical asymptote occurs at \(x = a\) if the denominator of a rational function is zero at \(x = a\) and the numerator is non - zero at \(x = a\).
For the function \(g(x)=\frac{1}{(x - 3)^2}\), set the denominator equal to zero: \((x - 3)^2=0\).

Step2: Solve the equation for \(x\)

Take the square root of both sides of the equation \((x - 3)^2=0\). We get \(x-3 = 0\), so \(x = 3\).
The numerator is \(1\), and when \(x = 3\), the numerator \(1
eq0\).

Answer:

A. The function has one vertical asymptote, \(x = 3\).