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...
|See 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.