Friday, May 27, 2011

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,

1. Let's say we have two equations $y_1=a$ for $x<0$ and $y_2=b$ for $x\geq 0$. Combine these two equations and we get one piecewise equation as below.

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'.
2. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
3. For the second piecewise equation
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.
4. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
5. For the third piecewise equation
,
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.
6. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Betty, Created with GeoGebra