# Modulus functions, graphs, transformations and inverses

Learn about modulus functions, graphs and transformations. Learn also about domains, ranges, inverses of modulus functions.

###### Author and programmer: Ron Barrow

UK Years 12-13, KS5, Core 3 (C3), Algebra and Functions

Instructions below    See also:   Reciprocal (Rational) Functions   PRINT

## How to Use this Applet

The applet on this page is designed to help you understand and visualise the behaviour of modulus functions and their graphs. The general modulus function has the form: A|Bx + C| + D. Varying A, B, C and D changes the graph. By investigating the effects of varying these different parameters, you should develop a feel for the behaviour of these very important functions, and for transformations of functions in general. You can show the domain and range of the function by clicking the checkboxes at the top of the page. You can restrict the domain by dragging the two little circles along the x-axis.
If you click "Show Inverse" you will be told if an inverse exists in the current domain. If it does exist it will be drawn for you. Playing around with these functions should help you understand the conditions for the existence of an inverse function. The rest of the instructions are easy to guess at, so I'll let you get on with it!
A challenge! Pressing "Random Curve" will generate a graph in yellow. Try to cover the yellow curve with the white one by adjusting the parameters. It's harder than it looks. Enjoy yourself!