Question

What are the horizontal asymptote rules?

Answer 1

To get horizontal asymptotes you must calculate two limits twice.
Your asymptote is represented as line `f(x) = ax+b`, where
`a = lim_(x->infty) f(x)/x`
`b = lim_(x->infty) f(x)-ax`

And the same limits must be calulacted in negative infinity to get appropiate result.

If more explanation needed - write in comments. I would add example later.