Question

How do you find all the asymptotes for function `y=2/(x-1)+ 1`?

Answer 1

First you make the denominator go to zero, later you make `x` go to infinity.

Explanation:

The first happens when `x` goes down to 1 and `y` will get larger and larger, or in the language:
`lim_(x->1+) y=oo`
bolded text
We also have `x` going up to 1 and `y` will be larger but negative:
`lim_(x->1-) y=-oo`

The second happens when `x` goes very large, either positive or negative. The first part will the go to `0` `y` will go to `1`
`lim_(x->+-oo) y=1`

Answer: `x=1andy=1`
graph{2/(x-1)+1 [-20.27, 20.26, -10.14, 10.13]}