The definition of junior middle school function is defined from [change relation]. If one quantity changes with another quantity, it is said that these two quantities have a functional relationship;

After the concept of set was introduced into high school function, the definition of function was also expanded. On the basis of the original two variables, a new concept called "correspondence rule" is added, and "correspondence rule" is generally represented by F.

At this point, the function can be defined as follows: let two variables x and y. If X changes and both have unique values corresponding to a corresponding law F, then X is called an independent variable, Y is a function of X, and F is their corresponding law (after introducing the corresponding law, the function of X can be directly written in the form of f(x)).

2. Different characteristics

Features of junior high school functions: junior high school functions only require

(1) Understand what a function is;

(2) The analytic formula of simple function can be found;

(3) can simply use various functions;

(4) You don't need to find the domain and value domain of each function.

High school functional characteristics:

(1) Study function definition (mapping) in depth;

(2) Mastering the application of various functions (including finding the analytical formula, defining the range and taking the value range); ?

(3) Being able to use the idea of function to solve related practical problems;

(5) Increase the synthesis between functions. In a word, function is a main thread running through middle school mathematics. In science study in middle school, we should use the viewpoint of function to solve related problems, especially practical problems.

3. Different thinking changes

Compared with junior high school function, the depth and breadth of knowledge learned in senior high school function have changed greatly, and the knowledge in junior high school is relatively shallow.

Function in senior high school: Pay more attention to the internal relationship of knowledge and its formation process, and require students to master the ins and outs of functions on the basis of understanding and memory, have a comprehensive understanding of what they have learned, and have higher requirements for students' abstract thinking and logical thinking.

4. Different in nature

Junior high school function: I mainly study monotonicity, parity, monotonicity, periodicity, symmetry, maximum and minimum;

High school function: and the high school function also adds a field to define and value.

References:

Baidu Encyclopedia-Function