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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.