Function Transformations in af(k(x-c))+d Form | Component Based Approach

Desmos Activity Builder doesn’t handle af(k(x-c))+d function transformations well.

However this Function Transformation Component will:

  • allow for any parent function f(x)
  • graph any transformation applied to f(x)

Two versions, one instant and the other animated. Looks like this:




  • No dependencies
  • Uses no deprecated features
  • Can be used with whatever correctness scheme you have in mind
  • It “just works” with little to no fiddling on your end

It’s not perfect… but it can pretty much replace everything that in the past relied on RawExpression transformations.

One application that comes to mind would be to refactor the Match My Transformation Activity that got deprecated some time ago.


That is just lovely.
There are so many different variables used for the parameters in these combined transformations.
I’ve seen af(b(x-c))+d and af(b(x-h))+k most often.
K is also used as a constant of variation, but I haven’t seen it “inside” the function; when algebra 1 students encounter a K they often think of Y value of a vertex for x^2 or abs(x), or the Y translation. Would you consider changing the K to a different letter?

Yeah I debated about that for a while. I was going to go with just a,b,c,d as there’s no mathematical reason to favour k for anything in particular, including for shifts.

That said, there’s a long history of using k for compression and stretching via physics analog for springs constants and elasticity. Technically it should be an omega but assuming unit mass it’s a decent approximation for the physical aspect of stretching that gives real meaning to what that parameter physically represents.

That said, it’s entirely up to you! Just change the letter k to b in the note and nothing at all changes for the calculations. Zero dependencies means you can modify a lot and not worry it’s going to break or anything.

Hope that helps

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Thanks so much for putting this together. I was able to use it in an self-paced activity for my students.

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Awesome, so glad it’s useful!