Question

How do you find all the asymptotes for function `2/(x-3)`?

Answer 1

We have two cases to investigate: what if the denominator becomes very small, and what if `x` becomes very great?

Explanation:

If `x-3=0->x=3` the whole function becomes very great (either positive or negative, or in the "language":

`lim_(x->3^-) F(x)=-oo` and `lim_(x->3+) F(x)=+oo`

If `x` goes very great (pos or neg) the function gets smaller, or:

`lim_(x->+-oo) F(x)=0`

So the asymptotes are `x=3and F(x)=0`
graph{2/(x-3) [-10, 10, -5.005, 4.995]}