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Topic: undefined points
Related Item: http://mathforum.org/mathtools/tool/35277/


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Subject:   undefined points
Author: Denn88
Date: Jan 19 2008
The review by Larry Denton raises an important point: for math tools to be
effective they need to accurately represent the situation being modeled.  

One of the reasons I created a rational expressions version of my algebra
visualization tools was my frustration in using graphing calculators to explore
rational expressions with students.  Graphing calculators typically misrepresent
both asymptotes and undefined points.  Both of these are correctly represented
in the rational equations visualizer.

Mr. Denton noted this for the general case of the function y=a(x-b)/(x-c)
where b is not equal to c.  However, for the case where b=c the discontinuity is
harder to spot.  The graph is identical to the line y=a with a point missing at
x=c.  A close look at the graph in the rational equations visualizer shows that
there is indeed a gap in the line at x=c.

Since Mr. Denton didn't see the gap and knew it should be there I expect that
many students would not notice it.  Because of this I have increased the size of
the gap to make it more readily apparent.  Some students may still fail to
notice the gap when they are exploring this tool.  If you are using this tool
with students be sure to ask them what the graph looks like when x is near or
equal to c, and what it looks like when b=c.

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