Question

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

Answer 1

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

Explanation:

As you cannot divide by 0
so `x-1!=0`
Also you calculate the limit when `x->oo`
`f(x)->3`
So `y=3` is a horizontal asymptote
See graph below
`f(x)=3 -3/(x-1)`
graph{(3x-6)/(x-1) [-10, 10, -5, 5]}