All About Functions

Date: 11/06/96 at 08:19:27
From: bonie
Subject: All About Functions

Hi Doc,

I would like a complete explanation of functions.

  Thanks a lot, Doc!

Date: 03/21/97 at 15:07:02
From: Doctor Matthew
Subject: Re: All About Functions

Functions are one of the most important ideas in mathematics. 

One of the most simple ways to think about functions is as a machine: 
you put something into the machine, and it spits something back out.  
For example, when I used to go to the zoo, they had these cool 
machines that would make plastic gorillas while you watched. You'd put 
three quarters into the machine and two minutes later a hot plastic 
gorilla would fall out of the machine. This is like a function: the 
input to the function was three quarters, and the output of the 
function was a plastic gorilla.  

So in general, a function is a set of rules for taking input and 
producing output. Most of the time when you talk about functions in 
math the input and output are numbers. If I've got a function called 
Fred, and I input the number 5, Fred might output 10. If I input the 
number 3, Fred might output 6. It just so happens that Fred is the 
"take a number and double it" function. You could write this as 
Fred(x) = 2x, which says that whatever the value of x is, the value of 
"Fred of x" will be twice it.

You could also imagine functions that take more than one number as 
their input, like f(x,y) = x+y. That means that if you give the 
function numbers 8 and 5 as input, the function spits out the number 
13 as output.

There's a lot more about functions out there, certainly lots more than 
we can tell you right now, but there's a lot more information in our 
archives.

Good luck!

-Doctors Matthew and Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/