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Topic: [math-learn] Introduction to functions
Replies: 30   Last Post: Dec 7, 2005 9:13 AM

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 Stephanie Kolitsch Posts: 21 Registered: 12/6/04
[math-learn] Introduction to functions
Posted: Nov 30, 2005 8:28 AM

I teach a college algebra class, which is designed as a service course
for most other disciplines at our University. One of the first topics
we cover is a short unit on functions. Even though these students are
supposed to know things like what constitutes a function, what the
domain of a function means, etc., most of my students react as if they
have never heard the word "domain". So I begin the lesson with a short
activity. I give them the definition of a function (if A and B are
nonempty sets, a function is a rule that assigns to each element of A
exactly one element of B). Then I set up an example using the people in
the classroom as the set A, the letters of the alphabet as the set B,
and the "rule" being that each person in the classroom is assigned the
first letter of his or her last name. Every person then tells me his or
her letter and I write it on the board. I identify the set of people as
the "domain", the set of letters as the "codomain", and the set of
letters I have written on the board as the "range". We make the points
that:

1. Every person participated (so every element in the domain is
assigned something).

2. No person participated more than once (so no element in the
domain was assigned more than one element in the codomain).

3. Some letters were used more than once (so elements in the
codomain can be repeated).

4. Some letters were not used (so elements in the codomain may
not be used, meaning that there is a difference in the "codomain" and
the "range".

We then go on to functions given as algebraic expressions, finding
domains of functions, graphs of functions, the vertical line test, etc.
My students seem to respond positively to this activity and the
fundamental characteristics of a function are implanted without any
references to "formulas" (which is what we deal with the most in our
college algebra class).

Now, after that lengthy introduction, here's my question: Do any of you
have any other quick, meaningful introductions to functions? I have
been using this particular example for a number of years, and I would
like to try something different. We do not discuss relations prior to
learning about functions, so any discussions we have in our class must
start from square one. The nature of our course prohibits any lengthy
discussions of any of our topics.

Stephanie Kolitsch

[Non-text portions of this message have been removed]

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Date Subject Author
11/30/05 Stephanie Kolitsch
11/30/05 John Clement
11/30/05 kirby urner
11/30/05 Stephanie Kolitsch
12/1/05 kirby urner
12/1/05 kirby urner
11/30/05 ArPeEs@aol.com
11/30/05 Richard Sisley
11/30/05 Wayne Bishop
12/1/05 John Clement
12/1/05 Wayne Bishop
12/1/05 John Clement
12/1/05 Wayne Bishop
12/1/05 John Clement
12/1/05 Ihor Charischak
12/2/05 Wayne Bishop
12/2/05 Ihor Charischak
12/2/05 Michael Paul Goldenberg
12/2/05 pamkgm7
12/2/05 pamkgm7
12/2/05 Ihor Charischak
12/2/05 Michael Paul Goldenberg
12/2/05 pamkgm7
12/2/05 Michael Paul Goldenberg
12/2/05 kirby urner
12/1/05 kirby urner
12/7/05 Antonija Horvatek
12/7/05 Wayne Bishop
12/7/05 Antonija Horvatek
12/7/05 Antonija Horvatek
12/7/05 Antonija Horvatek