Famously, functions can be represented in multiple ways: formula, graph, table. Less famously, function diagrams. These multiple representations offer multiple learning opportunities. On this page, I share some of the many lessons and activities I developed on the theme of recognizing functions.

**The basics:** Guess My Function

**From graph to formula:**Since the advent of electronic graphing, the high school math curriculum has included a greater emphasis on the multiple representations of functions, including especially graphing. That has been a welcome development, but in my view insufficient, and not always well executed. I wrote about the pedagogy of using electronically generated graphs in- Make These Designs

**From table to formula**: During my decades as a high school math teacher, I developed a fair amount of curriculum around the idea of*recognizing functions from data points*, a basic ingredient in mathematical modeling.- Functions from Tables: a blog post providing an overview of this topic, grades 4-11
- Constant Sums, Constant Products — a multi-level unit with content ranging from middle school to teachers' mathematics.
- `n^(th)` Power Variation | Teachers' Guide — a high school unit

**Hands-On Labs**- Perspective (inverse variation)
- Rolling Dice (exponential function)

**From function diagram to formula**- Nine Function Diagrams ("one-step" operations)
- Sixteen Function Diagrams (`y=mx+b`)
- Six Function Diagrams (Algebra 2) | Eight Function Diagrams (Precalculus)
- Name That Function! (interactive version of "Eight Function Diagrams")