What is a Function?

Date: 06/14/2001 at 01:30:26
From: Anjali
Subject: Algebra 2

I can't exactly understand the meaning of function. I mean I've read 
many definitions and I've asked many teachers, but I still don't 
completely understand. Is there a better definition you can give me? 

Thank you very much for your time.

Date: 06/14/2001 at 12:24:07
From: Doctor Peterson
Subject: Re: Algebra 2

Hi, Anjali,

There are many ways to define functions, depending on how precise we 
want to be, and how we are approaching the subject. But the basic idea 
is simple: a function is something that takes some sort of "input" 
(usually numbers in algebra, but it can be anything else), and for 
each possible input produces some "output." For example, any algebraic 
expression involving one or more variables can be seen as a function; 
for any set of values of the variables, the expression produces a 
single value. This expression is a function of a single variable x:

    3x - 1

We can explicitly call this a function by naming it (I'll call it "L" 
just to be different) and defining the value of the function for any 
input. We do this by stating that its value for any value of the input 
is the value of our expression when x has that value:

    L(x) = 3x - 1

This says that for any value of the variable x (the input), the value 
of the function (the output) is 3 times x, minus 1.

You don't have to use an expression like this to define a function; 
any description of how to get the output from the input will work. But 
this is the usual way you will see functions defined.

Here are some explanations I found in our archives that may help:

   All About Functions
   http://mathforum.org/dr.math/problems/bonie.11.6.96.html   

   Learning about functions
   http://mathforum.org/dr.math/problems/functions.html   

   Function Machine
   http://mathforum.org/dr.math/problems/johnson10.26.96.html   

   Functions and Function Tables
   http://mathforum.org/dr.math/problems/chris.05.11.99.html   

If none of these is clear to you, please write back and tell me what 
makes them hard to understand, or how you are confused.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/