# 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
$\text{E}=\text{D}+4$
,
where
**
$\text{E}$
**
= Emily's age, and
**
$\text{D}$
**
= Dan's age.

The quantities "Dan's age", "Emily's
age", "
**
$\text{D}$
**
", and "
**
$\text{E}$
**
" 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 $P\left(s\right)=4s$ gives the perimeter $P$ of a square with side length $s$ . Here $P\left(s\right)$ 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.