To illustrate the idea of a function let us define our line
with the equation . Graphically, a **function** is a rule that assigns
to each
x-coordinate defined exactly one y-coordinate. So a line containing the
points
(2,3) and (2,-3) would not be the graph of a function. An easy way to find
out if the graph of an equation is a function is to use the **vertical
line
test**. If a perfectly
vertical line crosses the graph of the given equation
at no more than one point,
then the equation is function.

Let's go back to our example. We can see the graph of in the following graph:

We can also plug one function into another in what is
known
as the **composition of functions**. Suppose we have two
functions, and . The composition the two functions: f circle g would look
like this:

What this means in terms of the two functions we have just defined, and , is that we put whatever is on the right side of , into each in . What this would look like with the actual numbers is:

The composition reversed would like: