I posted several GeoGebra files for function diagrams:
- to compare the function diagram of any function with its Cartesian graph.
- to illustrate the concept of composition of functions.
- to illustrate the concept of rate of change.
- to find the parameters of y=mx+b from the position of the function diagram focus.
- to solve a system of simultaneous linear equations with the help of two foci.
- to show that the in-out lines for y=1/x are all tangent to an ellipse.
There’s also a file that allows you to make function diagrams for printing or copy-pasting into a document.
All this can be found here — just click on GeoGebra. (There are also Texas Instrument eighty-something files, and Cabri files.)
Background on function diagrams: here.