From: Jeanne (for Teacher2Teacher Service)
Date: Mar 25, 2001 at 20:49:54
Subject: Re: determination of a relation to a function

Hi Kara,

I'd like to add to Marielouise's response by giving you a more informal way
of looking at functions.  This is a response I gave to a teacher a while ago
who was asking for ways of teaching functions.

I tell my students that a function is a rule that connects members from one
group to members of another group in a special way.  Each member of the first
group is paired with exactly one member of the second group.  We then go on
to discuss different situations of how this occurs.  The kids' favorite last
year is my Coke machine  description.  (Note: We had a vending machine that
sold bottled sodas for $1.)

     If you put in your dollar and push the button, the "functioning"
     vending machine will give you one bottle of soda.

     But you put in your dollar, push the button, and the vending machine
     gives you TWO bottles of soda, you are happy.  BUT the machine is NOT
     FUNCTIONING.


From here, we go on to ordered pairs. In a set of ordered pairs, if, let's
say an x-value of 1 is paired with the y-value 2 and 3, then the whole set of
ordered pairs is not a function.  This is to say that if the set contains the
ordered pairs (1,2) and (1,3), even if all of the other ordered pairs do not
repeat x values, the set is not that of a function.  (Note: x coordinate
matches the $, and the y coordinate matches soda.)  We classify several sets
of ordered pairs.

Then, we graph the different sets of ordered pairs that we have already
classified as functions and non-functions using our vending machine rule and
we look for patterns.  Given a little assistance, the students can see that
the non-functions have ordered pairs that give points that can be connected
with a vertical line.

From here we move on to graphs: circles, parabolas, lines, ...  and check
with the vertical line test.

Hope this helps.

 -Jeanne, for the T2T service

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