First , let's think about the left and right neighborhoods:

Here's what we've got -- see if you can figure it out!

Graph hug asymptotes.

These guys are functions.

He can ONLY cross the x-axis at x = 0.

Can he do this?

one possible function graph  ...  Buzz!  NOPE!  He'd have to cross the x-axis where he's not allowed to!


So, it must be like this:

The left and right neighborhoods for f( x ) = ( 3x ) / ( ( x - 2 )(x + 4 ) )