Looking for Clickable Transformations of Functions

My S’s are working on sequences of function transformations. I was wondering if anyone knows of, or has built, something that has transformations (say, “right 2”, “Stretch Vertically by 2”) that’s clickable so they can try the transformations in different order to see what happens.
TY you amazing CL people!

Here are a couple of ideas…

If you have something specific in mind. I could try to draft it up for your.


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Yea! Awesome!! Love both ideas.

How about something like this? Multiple Transformations • Activity Builder by Desmos Classroom


That’s fantastic! The function notation that gets built is amazing! As well as the animations. You an mxepstein have done great stuff.

Thanks - it was fun. I just added in a second screen that shows the history by color stamping successive transformations on the graph, and adding in the equation to a table (up to 10 in the table).

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I’ve been underwater with getting ready for finals, so I have not had a chance to come back and say how awesome this is! I’m pondering questions to pose to the S’s-- like:

  1. "Suppose transformation A is to reflect across the y-axis and transformation B is to move right 1. What happens to the graph of a function when you do this in different orders? (A then B compared to B then A?)
  2. Can you find two transformations whose order does not matter?
  3. Are there any other two transformations whose order does matter?
    Other ideas??

Hmm… maybe you can give them a before and after image and ask them to come up with possible sequences of transformations that could have worked. Maybe they have to find a way it could be done in 1 step, 2 steps, 3 steps, etc.

Also, in case it wasn’t clear, you can put a condition into the parent function (or make it a full piecewise function). This may make it easier to see horizontal reflections. I also just added in a 3rd screen where the axes shift instead of the graph.

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I’ve pondered approaching transformations via axes shifting before but never managed to work the approach all out. That third screen is awesome!

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Wondering some more about a trajectory for learning about transformations of functions. The patty paper idea-- allowing students to first create a graph of the function using patty paper feels productive. I’m wondering if anyone has modified the Desmos Patty Paper (Patty Paper Demo • Activity Builder by Desmos Classroom) to work with graphs of functions?

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