Func n' R: How to graph fancy functions!

What is a multiplicity? And how can it help?

How does a fancy function behave when it has an even # of roots?

How does a fancy function behave when it has an odd # of roots?

Trick! When I am given a graph, and need to find the function... what do I need to remember?

How many roots does f(x)=x^3-2x+1 have?

How many roots does f(x)=(x+2)^3(x-2) have? What is the multiplicity of each root?