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What is the analytic expression of the function?
Function is a rule! It can also be understood as law. This sentence is very important. Analytic function is similar to function formula, which is to find the functional relationship between functions X and Y. In a linear function, it is to find the value of k, that is, their relationship.

Resolution function is similar to function formula in finding the functional relationship between functions x and y ... in a linear function, it is to find the value of k, that is, the relationship between them.

Analytical formula of common functions:

Linear function y=kx+b

The proportional function (also a special linear function) y=kx.

Inverse proportional function y=k/x

Quadratic function y = a * x 2+b * x+c

Note: Generally speaking, a function reflects the direct (changing) relationship between two variables. Strictly speaking, a function is a correspondence (mapping) between two data sets. And "law" is first of all a (true) "proposition", which refers to the language form of expressing judgment in logic and is formed by connecting subject and object with a copula. For example, "Beijing is the capital of China" is a proposition. In modern philosophy, logic and linguistics, proposition refers to the semantics of a judgment (statement) (the concept of actual expression), which can be defined and observed. Proposition does not refer to judgment (statement) itself. Furthermore, "law" is the internal and essential connection among things, phenomena and processes. Law is different from theory, hypothesis, definition and theorem. It is an expression of objective facts and a conclusion accumulated through a large number of concrete objective facts and experiences. It is far from the concept of "function" and should not be confused.

In addition, the "expression" of a function should not be called "analytic expression" in general. Because many functions are not analytic (the concept of analytic is studied in courses such as "complex variable function" in universities), it is more appropriate to become "expressions" in order to avoid misuse.