If you're reading this guide now, you've probably dealt with functions in great detail already, so I'll just include some brief highlights you'll need to get started with calculus. Much of this should be review, so feel free to skip sections you feel comfortable with.

### Definition of a Function

A function is a rule that assigns to each element x from a set known as the "domain" a single element y from a set known as the "range". For example, the function y = x2 + 2 assigns the value y = 3 to x = 1, y = 6 to x = 2, and y = 11 to x = 3. Using this function, we can generate a set of ordered pairs of (x, y) including (1, 3),(2, 6), and (3, 11). We can also represent this function graphically, as shown below.

### The Vertical Line Test

Note that in the graph above, each element x is assigned a single value y. If a rule assigned more than one value y to a single element x, that rule could not be considered a function. As you may recall from precalc, we can test for this property using the vertical line test, where we see whether we can draw a vertical line that passes through more than one point on the graph: