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 = r2, 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 functions are periodic. See also density function; exponential function; hyperbolic function; inverse function; transcendental function.

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