How do you find all the asymptotes for function f(x) = (x+1) / (x+2)f(x)=x+1x+2?

1 Answer
May 31, 2015

Let's start with the vertical , the value that is "forbidden" for xx

Clearly that must be x=-2x=2 as this would make the denominator =0=0 and that is not allowed.

The horizontal is when xx becomes very large (either negative or positive). You will see that in that case the +1+1 and +2+2 will have a smaller and smaller effect on the outcome. So the whole thing tends to resemble

x/x~~1xx1 more and more, or: lim_(x->+-oo) (x+1)/(x+2)=1

So y=1 is the horizontal asymptote:
graph{(x+1)/(x+2) [-10, 10, -5, 5]}