question\nfind all vertical asymptotes of the following function.\n$f(x)=\\frac{2x - 18}{x - 3}$\nno…

question\nfind all vertical asymptotes of the following function.\n$f(x)=\\frac{2x - 18}{x - 3}$\nno vertical asymptotes\none vertical asymptote\ntwo vertical asymptotes\nno vertical asymptotes

question\nfind all vertical asymptotes of the following function.\n$f(x)=\\frac{2x - 18}{x - 3}$\nno vertical asymptotes\none vertical asymptote\ntwo vertical asymptotes\nno vertical asymptotes

Answer

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\neq0).

Answer:

One Vertical Asymptote ((x = 3))