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
as the composition of functions. Suppose we have two
functions, and . The composition the two functions: f circle g would look