Functions

A common term in mathematics is "function".  (Which tends to be displayed like f(x), which is to say the function of the variable "x".)  What is this?

A function is merely a way of explaining how two different numbers relate to each other, in mathematical form.

For instance, if we say y  = f(x), all that we're saying is that some mysterious value (y) can change.  And it changes in accordance with some other number that also changes (called x in this case).

For instance, we might say that distance in a car varies with time.  So distance (d) is a function of t (time).  So d = f(t). If we know that we're going at a constant speed, we might write d = s*t (or distance = speed times time).  Our description as to how this varies is a function.

Some of the time, something measurable might vary by more than *one* variable.  (i.e. if you hit a billiard ball, it's location might vary both by *when* you hit it, how hard you hit it, *and* the location you hit it in.  So we might get something like d = f(t, angle, force)

Pretty much anything you can express in numerical form can have a function attached to it.  Which is really handy for figuring out how things work. (i.e. where a ball goes when you hit it, how plants grow, how chemical reactions work, etc.)