Fun with Math!: Piecewise

A piecewise-defined function is a combination of at least two different functions at non-overlapping set of domain. The domain and range of the function is different for each one of them. For examples,

Let's say we have two equations y = a for x < 0 and y = b for x > 0. Combine these two equations and we get one piecewise equation as below.

$y=\left\{\begin{matrix} a, & x<0\\ b, & x\geqslant 0 \end{matrix}\right.$

Now, try to drag point A across y-axis. You'll find that point A will 'jump' from the left line to the right when x = 0. Now, click on 'View Domain' and you'll find that a pink point appears on the x-axis. If you drag point A away from the previous position, the pink points showing the domain on the x-axis. If you want to view the range on the y-axis, simply click on 'View Range'.

For the second piecewise equation

$y=\left\{\begin{matrix} ax+b, & 0\leqslant x\leqslant 1\\ -ax+b+2, & x>1 \end{matrix}\right.$ ,
perhaps you can move the values of a and b to view the changes of the graphs and also the domain and range. Likewise, click on 'View Domain', 'View Range' and drag point A to view the domain and range of the function.

For the third piecewise equation

$y=\left\{\begin{matrix} ax+b, & -3\leqslant x\leqslant 0\\ -ax+b, & 0<x<1\\ ax+b, & 1\leqslant x<3\\ b+5, & 3\leqslant x\leqslant 6 \end{matrix}\right.$ ,
try to change the values of a and b to view the changes happen to graph. Then, click on 'View Domain', 'View Range' and drag point A to view the domain and range of the function.

Betty, Created with GeoGebra

Fun with Math!

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Friday, May 27, 2011

Piecewise

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