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25 points each to the first two people to post here with an explanation of a function. (I think two answers is safer than just one, 0_o.) My text book says, "A function is a relation where for every x coordinate there is exactly one y coordinate. However, y coordinates can have more than one x coordinate. A special type of function where there is only one x for every y and only one y for every x is called a one to one function."

Er... what? It sounds like something they'd say on star trek while they're running around trying to eject the warp core before it explodes.

A function is a type of relation. All functions are relations, but not all relations are functions. What your book is talking about with x and y-coordinates are just independent and dependent variables. Basically, for every value that lines up with the x-axis (the independent variable), there can only be one value that lines up with the y-axis (the dependent variable), and vice versa.

If the terminology still makes your brain hurt, use the vertical line test. (That always made the most sense to me, because I'm very visual when it comes to math.) Look at the graph of the relation that you're trying to determine whether or not it's a function. If you can draw vertical lines on the graph and each line only intersects at one point, then it's a function. If there's, say, a parabola on its side, then the vertical line test would fail, because the line would run through two different y-values for the same x-value, and therefore cannot be a function.

Does that help at all?