Recognizing Functions

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Henri Picciotto

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")