Question

question
find all vertical asymptotes of the following function.
$f(x)=\frac{2x - 18}{x - 3}$
no vertical asymptotes
one vertical asymptote
two vertical asymptotes
no vertical asymptotes

Explanation:

Step1: Simplify the function

First, factor the numerator: \(2x - 18=2(x - 9)\). So the function becomes \(f(x)=\frac{2(x - 9)}{x - 3}\).

Step2: Find the vertical - asymptote condition

A vertical asymptote occurs when the denominator of a rational function is zero (after simplification, if there is no common factor between the numerator and the denominator). Set the denominator \(x - 3=0\), we get \(x = 3\). But when \(x = 3\), the numerator \(2(x - 9)=2(3 - 9)=-12
eq0\).

Answer:

One Vertical Asymptote (\(x = 3\))