# Variables

A variable is a symbol used to represent one or more numbers.  The numbers are called the values of the variable.

Example:

My sister Emily is 4 years older than me, so:

When I was 10, she was 10 + 4 = 14 .

When I was 17, she was 17 + 4 = 21 .

When I was (Dan's age), she was

(Dan's age) + 4.

We can say (Emily's age) = (Dan's age) + 4 ,

or simply E = D + 4 , where E = Emily's age, and D = Dan's age .

The quantities "Dan's age", "Emily's age", "D", and "E" are variables because they can represent many different numbers.

In a functional relationship, we say the dependent variable (usually y or f(x)) is a function of the independent variable (usually x). It is possible for a function to have more than one independent variable.

Example:

The function P(s) = 4s gives the perimeter P of a square with side length s. Here P(s) is the dependent variable, and s is the independent variable.

Usually, when graphing a function, the independent variable is graphed on the horizontal axis, and the dependent variable on the vertical axis.