Question

How do you find the horizontal asymptote `y = x / (x-3)`?

Answer 1

`y = x/(x-3) = 1 + 3/(x-3)`

Hence the horizontal asymptote is `y = 1`

Explanation:

`y = x/(x-3) = (x-3+3)/(x-3) = 1+3/(x-3)`

So as `x->+-oo, 3/(x-3) -> 0` and `1+3/(x-3) -> 1`

So the horizontal asymptote is `y=1`