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. ..

express

A function is a correspondence between sets. Then, we should understand that there is more than one functional relationship between A and B, and finally, we should focus on understanding the three elements of the function. The corresponding rules of functions are usually expressed by analytical expressions, but a large number of functional relationships can not be expressed by analytical expressions, but only by images, tables and other forms.

Extended data:

Origin of function

The word "function" used in China's math book is translated. Actually, it was Li, an algebra expert in Qing Dynasty, who translated "function" into "function" when he translated Algebra (1859).

In ancient China, the word "Xin" and the word "Han" were universal and both had the meaning of "Han". Li's definition is: "every formula contains heaven, which is a function of heaven." In ancient China, four words were used to represent four different unknowns or variables: heaven, earth, people and things. The meaning of this definition is: "Whenever a formula contains the variable X, the formula is called a function of X."

So "function" means that the formula contains variables. The exact definition of the equation we are talking about refers to the equation with unknowns. However, in the early mathematical monograph "Nine Chapters Arithmetic" in China, the term equation refers to simultaneous linear equations with many unknowns, that is, the so-called linear equations.