In this game you control a composed function T∘D (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).
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.
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.
This web site is based in part upon work supported by the National Science Foundation under NCSU IUSE award 1712280 (July 2017 through June 2019) and KCP Technologies DRK-12 award ID 0918733 (September 2009 through August 2013). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.