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

# function summary

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Below is the article summary. For the full article, see function.