Graphs of Functions and Symmetry: All in One

by Kanchan Manaktala

You might like to press F11 to view the Microworld in Full Screen mode.

In general, we tell the Mathematical Story above the Microworld, and place the Interaction Instructions below it.

The Story:

This delightful 6-page Microworld is a gentle introduction to the symmetries of a graph. It approaches this idea through the metaphor of reflection, as in reflection through a mirror. The basic reflections that it considers are: reflections through the x-axis and y-axis, and through the line y=x.

Beginning with reflections of points through these lines, it moves on to let the reader experiment with the reflections of graphs and curves through these lines, and gives a visual tour of the various notions of symmetry associated with these geometric operations.

Interaction Instructions:

The exploration pages have buttons that give explanations of the mathematical concept to be explored, as well as of the steps to take in the exploration.