Given a number set A, assuming that the element in it is X, now apply the corresponding rule F to the element X in A, and record it as f(x), and get another number set B. Assuming that the element in B is Y, the equivalent relationship between Y and X can be expressed as y=f(x).

This relationship is called functional relationship, or function for short. The concept of function includes three elements: definition field A, value field C and corresponding rule F, among which the core is corresponding rule F, which is the essential feature of 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, the function means that one quantity changes with another quantity, or that one quantity contains another quantity.

Extended data

The definition of function is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.

1, independent variable (function): a variable related to other quantities, and any value in this quantity can find a corresponding fixed value in other quantities.

2. Dependent variable (function): It changes with the change of independent variable. When the independent variable takes a unique value, the dependent variable (function) has and only has a unique value corresponding to it.

3. Function value: In the function where Y is X, X determines a value, and Y determines a value accordingly. When x takes a, y is determined as b, and b is called the function value of a. ..

Baidu Encyclopedia-Function