Horizontal asymptote question?

Question

To find these, you need to find the limit as x->+/- inf,

My question is, how do you know if there will be a + and - answer, (e.g. a horizontal asymptote at y=+2 and -2)

Can someone show me an example of when there is only a positive answer, and one where there is a positive and negative answer?

Answer 1

y = x/(x^2+1)^1/2 has horizontal asymptotes at y = +/- 1.

Y = x/(x+1) has only a positive asymptote at y= 1