Question

How to find the asymptotes of `f(x) = (x+2) /( 2x-5)`?

Answer 1

The asymptotes can be found by looking at `lim_(x->oo)` , `lim_(x->-oo)` and `lim_(f(x)->oo`

Explanation:

The asymptotes can be found by looking at `lim_(x->oo)` , `lim_(x->-oo)` and `lim_(f(x)->oo`

Looking at the last one first, `f(x) ->oo` as the denominator approaches zero. This occurs when `2x -> 5`. This means there is a vertical asymptote at `x = 5/2`

As `x` gets very large, either negatively or positively, `(x+2)/(2x-5) -> x/(2x) -> 1/2`
Thus there is a horizontal asymptote at `y=1/2`