MATLAB

The command funtool opens an interactive graphical function calculator that uses mouse clicks to perform operations on symbolic expressions. It can simultaneously manipulate and graph (in two separate windows) two functions $f(x)$ and $g(x)$ and allows constant horizontal shifts. A third window controls the calculator, and contains the symbolic functions f and g, the chosen domain of these functions, and a constant value a.

Below this are four rows of buttons that enable you to combine and operate on f and g in a variety of ways as well as controls for the calculator itself.

Try funtool when you have some time to help visualise how functions behave and interact.