The Symmetry of Functions

As I work with students to analyze graphs, I’ve noticed that many of them have trouble distinguishing whether a function is symmetric about the y-axis or the origin.

I designed this activity to animate the reflection of a function about the y-axis and the rotation of a function about the origin.  I chose to illustrate symmetry about the origin as a 180° rotation rather than a reflection through the point (0,0).  I think this is easier for the students to learn to visualize in their minds.

To rotate the curve, I defined the rotation using parametric equations.  Desmos has a great learning demo on parametrics here

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Here’s my activity:

Symmetry Activity

Feel free to duplicate it and try editing it to something useful for your classes!  (Remember, if you just click preview, you won’t be able to see anything in a hidden folder.  You’ll see it just like the kids will.)

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