In mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another (the dependent variable), which changes along with it.
Most functions are numerical; that is, a numerical input value is associated with a single numerical output value. The formula A = 03C0; r 2 , for example, assigns to each positive real number r the area A of a circle with a radius of that length. The symbols f (x) and g (x) are typically used for functions of the independent variable x . A multivariable function such as w = f (x, y) is a rule for deriving a single numerical value from more than one input value. A periodic function repeats values over fixed intervals. If f (x + k) = f (x) for any value of x , f is a periodic function with a period of length k (a constant). The trigonometric function s are periodic. See also density function ; exponential function ; hyperbolic function ; inverse function ; transcendental function .