You probably haven't seen these before, but they really do make ultra cool Calculus problems. I've seen them in most texts. They're really pretty easy if you look at them the right way.
** For this one lesson, I'll be dumping my usual color scheme. We'll be going with green for positive and red for negative. In the next lesson, we'll be back to normal.
First, let's really look at what absolute values do:
Absolute values leave positive numbers and zero alone... and make negative numbers positive!
So, with graphs... let's think about the y guys: