I use Desmos activities and graphs as a constructivist tool to allow my students to experiment and draw their own connections in mathematics. I will update this page with additional examples over time.

Function Transformations

This activity is appropriate in precalculus, after students have already explored individual horizontal and vertical transformations, and are ready to analyze a sequence of multiple transformations.

The solid graph of the function \(f(x)\) is shown below. The dashed graph is a second function, \(g(x)\), which is a transformation of \(f(x)\).

Find an expression for \(g(x)\) in terms of \(f(x)\). You can check your work by changing the expression in the Desmos graph below.

You may wish to try changing one thing at a time. Remember, what is the difference between \(f(x+1)\) and \(f(x)+1\)? What is the difference between writing \(f(-2x)\) and \(-2f(x)\)? You will need to use several transformations.