What are the steps for finding asymptotes of rational functions?

[mathdad]

Hello everyone. Time to get back to math. I have forgotten how to find asymptotes of rational functions. I think there are three types of asymptotes. Can someone show me how to find asymptotes of rational functions? What exactly is an asymptote?

 

[tkhunny]

Hello everyone. Time to get back to math. I have forgotten how to find asymptotes of rational functions. I think there are three types of asymptotes. Can someone show me how to find asymptotes of rational functions? What exactly is an asymptote?

There are many types of asymptotes. It depends on how you wish to classify them.

Vertical and Horizontal are the most easily recognized.

Oblique is next. Just a linear asymptote that is neither Vertical nor Horizontal.

After that, it is possible to group into just "Higher Order", or you may wish to classify as Quadratic, Cubic, Quartic, Quintic, etc.

We stretch the definition of Rational Function a little if we find anything other than a polynomial asymptote.

 

[mathdad]

I will post 3 questions tonight involving all three asymptotes.