Graphing Rational Functions

Graphing rational functions (where you have a polynomial in the numerator and another polynomial in the denominator) is a really hard concept for students to get - you are dealing with domains, with canceling out factors so that you get a different rational function that has a different domain ... and asymptotes galore! Vertical, horizontal, oblique ... and if you get a really tough one, you can even get a quadratic asymptote!!! It's enough to make even the toughest mathematician quiver in fear!

I made the following video to help my students "see" the math showing the algebra and then examining the tables and graph to see what the algebra really represents.

For other teachers, I used an IPad with the EQ Editor for a math editor, and MetaCalculator for my annotations. The video was created with ExpainEverything.

Disclaimer: I did make a mistake in the long division with the remainder - but with a video this long, it would take more time than it was worth to re-record the session. I decided to leave it because the mistake did not actually affect the oblique asymptote anyhow!
I hope this helps students (and even teachers who forget - like me -what they don't teach every day!)

Posted with Blogsy