Remember asymptotes?

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

graph of y = 1 / x  ...  the x and the y axes are asymptotesSee how the graph is getting closer and 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.