Remember end-tail behavior? What's going on with those tails?
This was called "finding limits."
One of the things math geeks get all jazzed about in Calculus is seeing what happens when and .
We can do this with these rational function critters, too. The key here is that horizontal (or slant) asymptote.
Check it out:
Remember... GRAPHS HUG ASYMPTOTES!
As x gets bigger and bigger (goes to the right), our graph gets closer and closer to that asymptote (which is y = 2.) It will never actually hit the asymptote ( f(x) will never = 2), it will just get closer and closer. This is why we use the word "approaches." It's the same story on the left when x is getting smaller and smaller.