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Exploring Function Diagrams with Cabri Applets by Henri Picciotto
For an introduction to function diagrams and their use in secondary math education, see Function Diagrams. To download Cabri dynamic geometry files and TI calculator programs, go to Function Diagrams: Electronic Tools.

Here are links to Cabri applets I created to help in the study of functions through animated and manipulable function diagrams. The notes below are intended to suggest a sequence of explorations and to provide a table of contents of the available applets. There are some instructions within the figures, and below them. You can explore further by dragging free points (often thick red points in the figures).

* An applet which allows you to simultaneously look at the function diagram and the Cartesian representation of a quadratic function.

* An applet which allows you to look at an example of the composition of two functions.

* Another one that shows the composition of a function and its inverse.

* An applet to dynamically find the linear function that corresponds to a given focus as you move the focus.

* Another one that includes the foci for two linear functions, and can be manipulated in the same way. It allows you to find the solution of a system of simultaneous linear equations in two variables by finding the common in-out line. It can also be used to find inverse linear functions by looking (manually) for foci in symmetric positions.

* An applet to explore magnification, or how the rate of change shows up in a function diagram. You can control the value of Δx, and see how it affects Δy/Δx.

* A sequence of eight animated function diagrams, which can provide a context for a discussion of domain, range, and rate of change. To evaluate the validity of the students' guesses about what functions are represented, the animation can be stopped, and the x can be dragged manually. (Suggested level: Precalculus, but would work at the end of some Algebra 2's or at the beginning of a Calculus course.)

* Two applets about the function diagram for y=1/x. One shows that the in-out lines are all tangent to an ellipse, the other is useful in proving this result.