Function and equation are two closely related mathematical concepts, and they permeate each other to form the idea of function and equation. The idea of function and equation has been fully reflected in the college entrance examination in recent years, so the application of function and equation is particularly important. The curriculum standard also points out that students should initially use the thought of function to understand and deal with simple problems in real life and society, and use the nature of beautiful numbers to find approximate solutions of equations to realize the organic connection between functions and equations.

The application of function in the knowledge of equations and inequalities;

In fact, algebra can be regarded as a functional expression with variables. To find the value of algebraic expression is to find the specific function value; Equation is actually to find the variable value of a known function that satisfies certain conditions, so that the known function has a pre-specified value on the variable value, especially the value of the independent variable when the function value is zero: inequality can be regarded as the error estimation of the function.

In this way, the equation and inequality are unified into the category of function, which embodies the unity of mathematics. One-dimensional quadratic equation and one-dimensional quadratic inequality can be regarded as special cases of studying quadratic functions and quadratic trinomials.

Function introduction:

Function is the correspondence between two sets of non-empty sets in mathematics: each element in the input value set can correspond to the only element in the output value set.

Its definition is usually divided into traditional definition and modern definition, the former from the perspective of movement change, the latter from the perspective of set and mapping. The concept of function contains three elements: definition domain A, value domain C and corresponding rule F.

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 they are called 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. ..