OK...  what were the 2 things?

 intercepts asymptotes

What were the 2 sentences?

 These guys are functions. Graphs hug asymptotes.

Let's do some graphing, baby!

 Graph 2 thingsand2 sentences!
 The y-intercept: Find f(0)
 The x-intercept: Set numerator = 0 and solve
 Since we only deal with real numbers when graphing, this has no solution!*Do you see why? This is going to be very useful info!
 Vertical asymptotes: Set denominator = 0 and solve
 Horizontal asymptote:
 Look at

Now we're ready to graph...  Remember that plotting points is for sissies, so use your brain!

First, let's get our intercepts and asymptotes on the graph:

 *Remember the the graph CANNOT cross the y-axis anywhere else and it CANNOT cross the x-axis at all!

Now, we use our brains and our sentences...

These are the three neighborhoods that this graph lives in:

Let's look at the left neighborhood:
*Remember your 2 sentences!

Since he's a function (and must pass the vertical line test), he can't do both.

What did we say about crossing the x-axis for this guy?  (Look back if you need to.)

Yep -- he's not allowed to cross the x-axis!  But, look at that bottom guy:

But, he's not allowed to -- so, he's got to live upstairs!

We can use the same reasoning for the right neighborhood:

What about the middle neighborhood?

And remember, he's not allowed to cross the x-axis!  So, he CAN'T do any of these things:

What's left?