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What is a function

You might be wondering what a function is and how to tell the difference between a function and a procedure.function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician

This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y. That is, f(x) can not have more than one value for the same x. To use the language of set theory, a function relates an element x to an element f(x) in another set. The set of values of x is called the domain of the function, and the set of values of f(x) generated by the values in the domain is called the range of the function. In addition to f(x), other abbreviated symbols such as g(x) and P(x) are often used to represent functions of the independent variable x, especially when the nature of the function is unknown or unspecified.

, gives the dependent variable A (the area) as a function of the independent variable r (the radius). Functions involving more than two variables (called multivariable or multivariate functions) also are common in mathematics, as can be seen in the formula for the area of a triangle, A = bh/2, which defines A as a function of both b (base) and h (height). In these examples, physical constraints force the independent variables to be positive numbers. When the independent variables are also allowed to take on negative values—thus, any real number—the functions are known as real-valued functions. (Source: www.britannica.com)