What is a function?

Function is a mathematical term. In algebraic expressions, each value of x corresponds to only one value of y, which means that y is a function of X.

The definition of function is usually divided into traditional definition and modern definition. The two definitions of functions are essentially the same, but the starting point of describing concepts is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.

The modern definition of a function is to give a number set A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another number set B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x). The concept of a function includes three elements: the domain A, the domain B and the corresponding rule F, among which the core is the corresponding rule F, which is the essential feature of the function relationship.

Function was originally translated by Li, a mathematician of Qing Dynasty in China, in his book Algebra. He translated this way because "whoever believes in this variable is the function of that variable", that is, a function means that one quantity changes with another, or a quantity.