Discussion:  Roundtable 
Topic:  Teaching the Concept of Functions 
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Subject:  RE: Teaching the Concept of Functions 
Author:  Craig 
Date:  Sep 23 2004 
I have a very most wonderful favorite reference for functions: it's Unit 6 of
Year 1 in the Math Connections series. There are lots of rich analogies,
including the "fingerprint" function, mapping a fingerprint to a person [not
invertible, since the average person has 10 different fingerprints]; the ZIP
code function, mapping a letter addressed with a zip code to a post office [also
not invertible]; and license plate function, mapping a license plate to a
particular car [this one is invertible].
Other function analogies I have used include speeding fine as a function of mph
over the speed limit, what kind of soda comes out of the machine as a function
of which button was pressed, elevation above sea level as a function of location
(great with a topographical map www.topozone.com ), distance between two
points as a function of their coordinates, the Platonic soliddual
relationship [Dual(square) = octahedron, Dual(tetrahedron) = tetrahedron,
etc.].
As for function composition, what about this:
A teenager's spending money S one week is a function of how many hours h
worked the previous week, say S = f(h)
If the teenager has less than $20, she will not go to the movies. If she
has $20 or more, but less than $30, she will go to see one movie this weekend.
If she has $30 or more, she will go to two movies this weekend. If M = number
of movies, then M = g(S).
The composite function gOf(h) = g(f(h)) gives the number of movies as a
function of the number of hours worked.
 
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