First, expand the information.
Function, a mathematical term. Its definition is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.
The modern definition of a function is to give a set of numbers A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another set of numbers B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x).
The concept of function consists of three elements: domain A, range B and corresponding rule F, among which the core is corresponding rule F, which is the essential feature of function relationship.
Function was originally translated by Li, a mathematician of Qing Dynasty in China, in his book Algebra. He translated this way because "whoever believes in this variable is the function of that variable", that is, the function means that one quantity changes with another quantity, or that one quantity contains another quantity.
Second, the expression method
1. Analytical formula method
The method of expressing the functional relationship between two variables with an equation containing mathematical relationship is called analytical method. The advantage of this method is that it can express the quantitative relationship between function and independent variable concisely, accurately and clearly. The disadvantage is that it is often complicated to calculate the corresponding value, and some functional relationships in practical problems may not be expressed by expressions.
2. List method
The method of expressing the functional relationship between two variables by list method is called list method. The advantage of this method is that the corresponding function values can be read directly by knowing the values of the independent variables in the table; The disadvantage is that only some corresponding values can be listed and it is difficult to reflect the whole picture of the function.
3. Language narrative method
Describe the relationship between functions in language.