Mapping Functions in the Real World

Date: 20 Mar 1995 10:23:47 -0500
From: Maxine Fuentes
Subject: functions

Dear Sir:
        What is the purpose of learning to map a function? 
What is it used for in the real world? 

                                    Thank you,
                                    Wayne Claire Elizee
                                    St. Thomas, Virgin Islands

Date: 20 Mar 1995 10:35:19 -0500
From: Dr. Ken
Subject: Re: functions

Hello there!

Well, the way I see it, learning to deal with functions 
is really learning a new way of thinking about the world.  
Learning to map a function is just one of the essential 
tools you need to use if you're going to deal with functions.

Perhaps you've seen (in movies or whatever) business 
office meetings in which someone brings in a huge graph 
of the company's sales for the past year.  Well, those big 
graphs are graphs of _functions_, like sales as a function 
of time.  So the ability to read a graph and get information 
from it is really quite valuable.

What's more, if you plan to do more math beyond the class 
you're taking now (which I sincerely hope you do!!!), you'll 
really need to know those functions cold.  

Here's one practical example of a famous real-world problem
that uses functions:  Farmer Bob wants to build a pen to
keep his pigs in.  He's got 16 Feet of fence, and he wants
to use it to build the largest possible pen (i.e., the one
with the most area).  What shape should he build his pen
in?  Well, it turns out that the correct answer is to make
it a circle.  This is somewhat hard to prove (and yes, the
proof involves functions!).  But what if we say that the
pen has to be some kind of rectangle?  Then to find the
best kind of rectangle, it turns out that you can look at
the graph of the area function f(x) = x(8-x), and find
where it hits its maximum value.  Then you've got it. 

-Ken "Dr." Math