graph the function. plot all necessary asymptotes. for vertical asymptotes, make sure there are at least two…

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0. $x - 2=0$, so $x = 2$ is vertical asymptote.

Step2: Find horizontal asymptote

Since degree of numerator and denominator are same, divide leading - coefficients. Leading coefficient of numerator is 1 and of denominator is 1. So $y = 1$ is horizontal asymptote.

Step3: Find points on the graph

When $x=0$, $f(0)=\frac{0 - 6}{0 - 2}=\frac{-6}{-2}=3$. When $x = 1$, $f(1)=\frac{1 - 6}{1 - 2}=\frac{-5}{-1}=5$. When $x=3$, $f(3)=\frac{3 - 6}{3 - 2}=\frac{-3}{1}=-3$. When $x = 4$, $f(4)=\frac{4 - 6}{4 - 2}=\frac{-2}{2}=-1$.

Answer:

Vertical asymptote: $x = 2$, Horizontal asymptote: $y = 1$. Plot points $(0,3),(1,5),(3, - 3),(4,-1)$ and draw the hyper - bolic graph approaching the asymptotes.