Thinking about teaching functions in the next few weeks (to UK Year 12 ages 16-17) I realised that I could use Desmos to illustrate composite functions; the following slideshow illustrates the syntax.

We can also use Desmos to illustrate a function and its inverse. To create the page below (select the image), I started with a **graph already online **illustrating the general case of a quadratic function and its inverse and simplified it. f(x) and g(x) can be changed to a different function and its inverse. Note that the domain of f(x) can be changed.

Further examples: **exponential function **and** basic quadratic **(where we need to restrict the domain for an inverse function to exist).

Staying with Desmos, as I have mentioned before, the function notation is excellent for transformations:

(See **this page** for all Desmos slideshaows).

It is also possible to define a function with more than one argument and use Desmos as a calculator

For some clear examples and a resource to point students to, **Functions** from The University of Plymouth **Mathematics Support Materials** is useful. The format used in this series makes the examples clear and all the exercises given have answers.

Other useful resources (requires Java) include the **Wisweb applets**, algebra arrows could be used to demonstrate functions and their inverses as shown in the following images.