Question

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

Answer 1

First look at what makes the denominator `=0`

Explanation:

When `x` gets closer to `-1`, either from below, or from above, the denominator will get closer to zero, and the function as a whole will get larger and larger.

Or in "the language":

`lim_(x->-1^+) y= oo and lim_(x->-1^-) y= -oo`

This is called the vertical asymptote `x=-1`

The horizontal asymptote is when `x` becomes incredibly large, either negative or positive. In this case `y` will be smaller and smaller, or:

`lim_(x->oo) y=0 and lim_(x->-oo) y=0`
So the horizontal asymptote is `y=0`
graph{2/(x+1) [-28.86, 28.9, -14.43, 14.43]}