Limit Definition of the Derivative- Multiple Representation Reference Sheet

I pinned this picture years ago when I started teaching calculus and it's stuck with me every year. It's so simple and clean, but shows exactly where we came from and where we're going. Math is so elegant sometimes *sighhhhhhh*. 

I really want my students this year to make concrete connections between representations as often as possible. The limit definition of the derivative is such a foundational and, at its core, simple concept. It's slope. We know slope. 

I made this reference sheet for my kids to get them talking, thinking, and connecting between representations of the derivative. I have them start with their Algebra I definition of slope, then progress through notational changes to derive the formula for slope of the tangent line. I've included the general formula on the front and the definition at a point on the back. 

I'm  giving this as a warm up in class tomorrow so I know I'll be tweaking, but if you see anything you think should be tweaked leave a comment! 

Limit Definition of Derivative- Multiple Representation Reference 

UPDATE: Here is my filled in key from class! I really liked this and will incorporate it again next year for sure! 

Limit Definition of Derivatives KEY