Piecewise Functions

Thanks to Alex Beltechi for this tutorial on PSD Tuts.

This is the first graphic that I needed Adobe Illustrator to complete.  Also, it was the first that took me multiple sessions to complete.  I really like the effect for piecewise functions though.  I always teach this topic by describing piecewise functions as a combination of different parts of multiple functions.  We start by graphing each individual rule and highlighting the parts of each that will be used for the new function (as specified by the domain).  This illustration gives a good starting point for the discussion as each letter is a piece of the complete word.  Something of a simple idea, but that's definitely where we want to start with piecewise functions.

Power Rule

Thanks to Arik for this tutorial on PSD Tuts.

I really liked the look of this text effect when looking through tutorials so I used it for the Power Rule.  The power rule is usually the first lesson in Calculus, after limits and the definition of derivative, where students really start to see the beauty and ease of the subject.  It's an exciting lesson indeed!