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Discussion: All Tools in PreCalculus on TI Calculator
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
> I think graphing the piecewise
> 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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