(beginning calculus) I need help finding a limit of this graph

Here's the graph i drew
http://tinypic.com/r/26oaf/7

(the black part is the actual graph, the gray is the asymptotes)

I need help finding the lim of this graph as x approaches infinity?

Also, it would be great additional help if you could explain how you found that limit.
I'm confused. ):

Are you sure about the graph? Were you given the graph, or a function?
With rational functions, you cant have two different horizontal asymptotes...but maybe it was a piece function?

Anyway, when x is approaching infinity, you are looking as far to the right as possible. Infinity means positive infinity. Then where are the y values?

The graph as given is getting closer to the x axis, so y is approaching zero.

Lim=0 as x-> inf.

Then as x approaches neg infinity, the limit is 2, since the left side of the graph is getting closer to 2.

But if the horizontal asymptote is actually the line y = 2, then the graph is dropping down too far, and the limit is 2.

Hoping this helps!

Remember that a limit tells you what something would be if you could use standard math tecniques to find it out. You cannot do this for x = inifinity so you need to use a limit?

Where does y go as x -> inf? Well the graph is decreasing and it is a hyperbola. So y goes to 0 because x = 0 is an asymptote as x -> inf.