1Zrelations

Relations and Functions

A ** relation ** is any rule, list or graph that connects two (or more) variables (usually x and y).

A ** function ** is any relation that only has one y-value for any x-value. Most of our course is about functions.

We use the ** vertical line test ** on a graph to test if the relation is a function. If there is __**no**__ vertical line that hits the graph more than once, then the relation is a function.

For example, the equation y = x 2 (a parabola) is a relation because it links x and y together __and__ it is a function because for any x value there is only one y value. (it passes the vertical line test)

On the other hand, x 2 + y 2 = 16 (a circle) is a relation but not a function because values in the domain –4 to +4 have two y-values. (it fails the vertical line test)


 * Example **

The equation y 2 = x produces a sideways parabola. It fails the vertical line test so it is a relation but not a function.