**I'll start by showing you the traditional method, but then I'll explain what's really going on and show you how you can do it in your head. It'll be easy!**

**Given some polynomial guy**

If | , then the x-axis is the horizontal asymptote. | ||

If | , then the horizontal asymptote is the line | ||

If | , then there is no horizontal asymptote. (There is a slant diagonal or oblique asymptote.) |

**Yeah, yeah, you COULD just memorize these things... but it's way better to KNOW what's going on. Then you can just do it.**

**What we're really doing is some quick long division to divide the denominator into the numerator. The cool thing is that we only need to do the first part -- no remainder crud! And we can do it in our heads!**