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There are a number of ways that the calculator can help with this. Examples
are given below but others will no doubt occur to experienced teachers.
(i)
Rational functions can be investigated using the
NUM view. For example, enter the functions
F1(X)=X+2 and F2(X)=(X
will elicit the fact that they are 'identical'
algebraically but what then about the point X=2 in the NUM view (see
right)? Use this in discussion to introduce the convention of graphing
with a 'hole'.
You can also have a great deal of fun with the
class by telling them to un
to zoom in repeatedly on X=2 in the PLOT view
in an effort to "find the hole". They won't of
course, but you can laugh watching them and
then discuss why they didn't - a good way to
introduce the idea of limits!
However - there is a trick to this! If you use the default axes of -6.5
to 6.5 then there will be a hole (see right) because x=2 falls on a pixel
point and so, since it is undefined, the calculator leaves it out.
For this to work you need to
sabotage their efforts in
advance via a scale which does not have x=2 on
a pixel. Starting with a scale like this ensures
that subsequent box zooms won't produce the
"hole". A good scale is -1 to 6 on both axes and
you can rationalize the choice by telling them that it "focuses well on
the point we're interested in". They may still sabotage this by choosing
their own axes when zooming.
(ii)
When discussing the
concept of a domain, the
NUM view can be very useful
in developing this (see right).
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-4)/(X-2). Discussion
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F1(X) and then
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