Functions:  The Representation and Synonym Games
or
Knowing the lingo to stay in the club

Have you ever noticed the way organizations and clubs develop their own words and symbols for the things that are important to the club.  This gives the club an easy way to talk and write about the important things.  Unfortunately (or fortunately for secret clubs), people outside the club can't understand what the club members are saying when they are using their club language.  In mathematics, ways of showing information, terminology, and symbols are developed to make things more convenient for those using the information.  Convenient that is, if you know what everything stands for.  Especially with functions, understanding what the representations, words, and symbols mean is the major key to "staying in the club."

A function is a rule in which each input has exactly one output.

The Representation Game
Functions are represented (shown or displayed) in many ways.  One function usually has more than one representation, and looking at different representations of the function helps you get more information about the function.  Useful representations of a function include:  graph, table, formula or equation, list of ordered pairs, parallel number lines, or mapping diagram.  Keep in mind, changing the representation does not change the function, it just gives it a new look.

The Synonym Game
There are many ways to refer to the input and output values of a function.  Depending on the desired emphasis, various terms are used.  For example, if the input value is a number from an ordered pair, it is often referred to as a first coordinate.  If the input value is a replacement for x in an equation, it is often referred to as an x-value.

All of the following may be used to refer to an input value of a function:
	input			first component		first coordinate		x-coordinate
	x-value		value of the domain	domain element		argument
	input value		independent variable

All of the following may be used to refer to an output value of a function:
	output		second component	second coordinate		y-coordinate	
	y-value 		f(x)-value			value of the range			range element		
	output value	function value		dependent variable