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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 ) = 4 s 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.