In high school, we have learned the common representation methods of functions ( list method, image method and analytical method ) , which are further summarized and expanded as follows:

　　1. List method: A method of tabulating the values of independent variables and their corresponding function values.

　　2. Image method: A method of expressing functional relationships 　through intuitive images in a coordinate system .

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　　3. Analytical method(formula method)  A method of expressing the relationship between independent variables and dependent variables using mathematical expressions (also called analytical expressions) . According to the different forms of analytic expressions of functions, functions can also be divided into three types: explicit functions, implicit functions and piecewise functions:

　　(1)  Explicit function: The function is directly represented by the analytical expression of .

　　For example, , , , etc.

　　(2)  Implicit function: The corresponding relationship between the independent variable and the dependent variable is given by the equation

to make sure. For example:

, ,

But the explicit function of the latter is expressed as

.

　　(3) Piecewise function: A functiondomain. In high school, we initially learned about piecewise functions, their domains and images , among which the absolute value function is an example of a piecewise function.