# Piecewise and Absolute Value Functions

### Piecewise-Defined Functions

### Video

This video from *Khan Academy* shows how to evaluate piecewise-defined functions, both from the definition and by examining their graphs.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

This video from *patrickJMT* shows how to plot the graph of a piecewise-defined function given its definition.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

### Notes

These notes from the maths support centre SUMS at NUI Galway introduce piecewise-defined functions and some examples of those. Work through the exercises on Pages 3-4.

One example is the absolute value function (introduced on Page 5). You will find more about this function here.

A pdf of this document can be downloaded here.

### The Absolute Value Function

### Video

This video from *patrickJMT* gives an introduction to the absolute value of a number and some examples manipulating expressions involving the absolute value.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

This video from *Khan Academy* goes a bit further into absolute value functions and shows how to plot the graphs of more complicated absolute value functions.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

### Notes

These notes from *MathCentre* give a brief overview of the absolute value (modulus) function.

A pdf of this document can be downloaded here.

### Interactive Exercises

Plot the graph of the absolute value function $f(x)=|x|$ by inputting $y = \text{abs}(x)$ in the GeoGebra graphing software below. Try to adjust the function by adding a constant to $x$ inside the absolute value function, e.g. $|x-2|$, add a constant to the absolute value function itself, e.g. $|x|+3$, or multiply by a constant, e.g. $2|x|$. Examine the effect these transformations have on the graph. You can also combine these transformations and see what happens.

Please click here to view this calculator in another window.