# How do you identify all asymptotes or holes for f(x)=(3x-6)/(x-1)?

Oct 18, 2016

A vertical asymptote is $x = 1$
A horizontal asymptote is $y = 3$

#### Explanation:

As you cannot divide by 0
so $x - 1 \ne 0$
Also you calculate the limit when $x \to \infty$
$f \left(x\right) \to 3$
So $y = 3$ is a horizontal asymptote
See graph below
$f \left(x\right) = 3 - \frac{3}{x - 1}$
graph{(3x-6)/(x-1) [-10, 10, -5, 5]}