This applet is designed to help you understand inverse functions, and their domains and ranges, by looking at quadratic graphs.
There are buttons at the bottom of the screen to enable you to change the function, which is y = ax² + bx + c. The "Reset" button returns you to the beginning, y = x².

The two red dots at the ends of the x-axis can be dragged with your mouse. This restricts the domain of the function. If the "Inverse" box is checked then when the function is one-to-one an inverse function will be drawn.
Play around!