Before we actually try to graph a rational function, it would be nice to remember what these things are!

They're those guys like

f ( x ) = ( x^2 - x - 6 ) / ( x^2 - 1 )

Where you have a polynomial over another polynomial.

To graph these, we'll need

2 things and 2 sentences

That's it!

Here are the 2 things:





Here are the 2 sentences:


These guys are functions.


Graphs hug asymptotes.

Don't worry -- the next sections will tell you what these things mean.  Until then, memorize this! 

Since plotting points is for sissies, it will be our personal challenge to graph these things ONLY using the 2 things and the 2 sentences.  Oh, and one more thing: our brains!

*Note:  Until you learn Calculus, we'll really just be able to get rough sketches of these things.  Calculus will give you other stuff to really nail them!