How to find the asymptotes of f(x) = (x+2) /( 2x-5)f(x)=x+22x5?

1 Answer
Jan 15, 2016

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