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Rational Functions - The Whole Thing

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 ) )