Introduction to Functions

What is a function?

A function is a rule that takes one number as input and gives a single number as output. The input is called the independent variable because it can take any value in the domain of the function. The output value of the function is called the dependent variable since its value depends on the value of the independent (input) variable. Functions can be written as tables of input and output values, equations or graphs.

Example 1   The table:

Input	Output
1	5
2	6
3	7
4	8

defines a function since for each input value there is only one output value.

Example 2   The equation y=x+4 is a function since for each value of x you only get one value for y.

If x = 1 we have,

y	= 1+4
	= 5

If x = 2 we have,

y	= 2+4
	= 6

If x = 3 we have,

	y	= 3+4
		= 7

Example 3   This graph is another way to represent a function.

Note: The above examples are all different ways to represent the same function.

Example 4   The table

Input	Output
1	1
2	3
2	7
5	8

is not a function since it assigns two different values to the input 2.

The idea of a function is very important in mathematics. Algebra is basically the study of functions. Sometimes if we want to say that y is a function of x we write y=f(x).

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