Technologically Embodied
Geometric Functions
Cartesian Games

This page supports the Connect to Cartesian activity from the Connecting Geometry and Algebra Through Functions unit.


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

  • When you're finished with a round, press the Reset button to reset the counters to zero and start another round.
  • You can only change levels at the beginning of a new round.
  • At Level 1, the values are always integers. At higher levels, they can be fractions, so you have to be more accurate at higher levels.
  • On page 2 is a Cartesian coordinate system with both dependent variables plotted on the vertical axis. The independent variable x is always varying, and your job is to adjust s and v so that T(D(x) exactly matches ??(x).
  • When you have T(D(x) exactly matching ??(x), press the Check button.
  • On pages 3 and 4 the two functions TD and ?? are being graphed. You can use the traced graphs, or the points (x, T(D(x))) and (x, ??(x)) to observe the relative motion and adjust s and v correctly.
  • On page 5 you see only the graphs and the graphed points that are making them, but not the dependent variables themselves.
  • On page 6 nothing is moving, but you can drag x yourself to use the graphed points, and the values of the variables, to figure out how to adjust s and v.
  • On page 7, you have to figure out how to adjust s and vcorrectly without seeing the results until you press the Check button.
  • If you can succeed on page 7 at Level 4, you’re a real Expert!


Return to the Connect to Cartesian activity.     

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Update History:

01 April 2016: Updated to 4.5.0
21 October 2015: Created this page.