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.

Functional concept:

In the process of a change, the quantity that changes is called a variable (in mathematics, the variable is X, and Y changes with the change of the value of X), and some numerical values do not change with the variable, so we call them constants.

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

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.

Function value: in a 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. ..