Technologically Embodied
Geometric Functions
Dynagraph Game

This page supports the Dynagraph activity from the Cartesian Connections unit.


In this game you control a composed function TD (Translation following Dilation) by adjusting the dilation scale factor `s` and the translation vector `v`. The challenge is to make your function match a mystery function.

  • On page 2 you control independent variable x as well as `s` and `v`, so you have to vary `x` back and forth to see how you’re doing.
  • On page 3 independent variable `x` is always varying, so you only have to adjust `s` and `v`, but you have to watch carefully because `x` is flying along pretty quickly.
  • On either page, you can tell when you've solved the problem and discovered the mystery function, because the two dependent variables will be moving exactly together, connected by a green segment.
  • Once you've solved the mystery, press the Check button to get credit for your solution, and to get a new problem.
  • When you're all done, press the Reset button to reset the counters to zero for another round.
  • You can only change levels at the beginning of a new round.
  • Use pages 4 and 5 to play the same game using the form `f(x) = m x + b`.
  • Values for s and v are multiples of 1 (Level 1), 0.5 (Level 2), 0.2 (Level 3), or 0.1 (Level 4).


Go to the Create a Dynagraph activity.     


The term dynagraph was coined by Paul Goldenberg, Philip Lewis, and James O’Keefe in their study “Dynamic Representation and the Development of a Process Understanding of Functions” published by Education Development Center, Inc., and supported in part by a grant from the National Science Foundation.

Release Information and Rights

Update History:

05 March 2017: Added pp. 4 and 5 for `f(x) = mx + b`
01 April 2016: Updated to 4.5.0
21 October 2015: Created this page.