Definition of function: Given a number set A, let the element in it be X, and now apply the corresponding rule F to the element X in A, and record it as f(x) to 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). We call this relationship a 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.

Extended data

express

First of all, we should understand that a function is the corresponding relationship 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 can be expressed by images, tables and so on? .

concept

In the process of a change, the quantity that changes is called a variable (in mathematics, it is often X, and Y changes with the change of X value), 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? .

Mapping definition

Suppose a and b are two non-empty sets, if according to some correspondence? For any element A in set A, there is only one element B corresponding to it in set B. Then, such correspondence (including sets A and B, and the correspondence F from set A to set B) is called the mapping from set A to set B, and is recorded as? . Where b is called the image of a under the mapping f, and it is recorded as:? ; A is called the original image of B with respect to the mapping f, and the set of images of all elements in set A is denoted as f(A).

Then there is: the mapping defined between non-empty number sets is called a function. The independent variable of a function is a special original image, and the dependent variable is a special image?

Geometric meaning

Functions are related to inequalities and equations (elementary functions). Let the function value be equal to zero. From a geometric point of view, the value of the corresponding independent variable is the abscissa of the intersection of the image and the X axis. From the algebraic point of view, the corresponding independent variable is the solution of the equation. In addition, replacing "=" in the expression of a function (except a function without expression) with "",and then replacing "y" with other algebraic expressions, the function becomes an inequality, and the value range of the independent variable can be found.

set theory

What about the binary relationship between x and y? , for each one? , only one? , manufacturing? , and then call f an x to y function, write it down as follows:

Reference Function (Mathematical Function) _ Baidu Encyclopedia?