Did I just hear you say, "What the heck is an asymptote and why am I started to get all sweaty and twitchy?"


We've got that sentence:

Graphs hug asymptotes.

What does it mean?

Let's check out one of our old friends...

f ( x ) = 1 / x

a graph of y = 1 / x ... the x and y axes are asymptotesSee how the graph is getting closer to the axes?...  But, it will never touch them?

The x and y axes are asymptotes!

Asymptotes are lines (usually invisible) in space that a graph gets closer and closer to but never touches...

Graphs hug asymptotes.

OK, so for vertical asymptotes...

Set the denominator = 0 and solve.

This is like finding the bad spots in the domain.  It's where the function cannot exist.