| Discussion: | All Topics |
| Topic: | How to disconnect a piecewise graph |
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| Subject: | RE: How to disconnect a piecewise graph |
| Author: | stek |
| Date: | Mar 5 2007 |
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> functions on the TIs is a great visual that I can add to my
> instruction next year. Are there any other tools or advice when
> teacing piecewise functions?
If you want to graph a piecewise function with Sketchpad, there are several
resources available.
For a piecewise function consisting of two functions with a boundary, the
Advanced_Tools.gsp sketch from the Sketchpad Advanced Sketch Gallery contains a
tool that's pretty easy to use. Here's the URL:
http://www.dynamicgeometry.com/general_resources/advanced_sketch_gallery
For more than two functions, Paul Kunkel has put together tools for piecewise
functions of 2, 3, 4, or 5 pieces. Write me off-list if you'd like a copy of
these. I don't believe Paul has posted these on his site, so I will email him
suggesting that he do so. (His site is www.whistleralley.com. )
Jim Wilson from the University of Georgia has a Piecewise Linear Function
activity available online, at:
http://jwilson.coe.uga.edu/EMT668/EMAT6680.Folders/Kastberg/EMAT%206690%20Curriculum%20Unit/lesson%204%20piecewise%20fun./investigations/p%20inv%201%20d&r%20of%20plfunction/p%20inv1%20d&r%20of%20plfunction.html
Finally, if you want to create your own piecewise functions without using such
specialized tools, you will find useful the Boolean tools on the Advanced Sketch
Gallery:
http://www.dynamicgeometry.com/general_resources/advanced_sketch_gallery )
The Boolean tools are useful in creating expressions such as this:
if (x >= x1) and (x < x2) then use f(x)
if (x >= x2) and (x < x3) then use g(x)
To actually do this in Sketchpad, you first use the Boolean tools to create the
two Boolean expressions:
(x >= x1) AND (x < x2)
(x >= x2) AND (x < x3)
These expressions evaluate to 1 if true, or to 0 if false. You then graph a new
function h(x) based on f(x) and g(x):
h(x) = f(x) * ((x >= x1) AND (x < x2)) + g(x) * ((x >= x2) AND (x <
x3))
Enjoy,
Scott
Scott Steketee
Sketchpad Projects
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