1. Method introduction

Definition: For any X in the domain A of f(x), if F (-x) =-f(x), then f(x) is odd function; If both have f (-x) = f(x), then f(x) is an even function. Sum (difference) method: If f(x)-f(-x)=2f(x), then f(x) is odd function. If f(x)+f(-x)=2f(x), then f(x) is an even function.

Judging from commercial law: if f(-x)÷f(x)=- 1, then f(x) is odd function. If f(-x)÷f(x)= 1, then f(x) is an even function. Image judgment method: the image of odd function is symmetrical about the origin center, and the image of even function is symmetrical about Y axis.

2. Function introduction

Function, mathematical terminology. 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 number set 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 number set 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 a function includes three elements: the domain A, the domain B and the corresponding rule F, among which the core is the corresponding rule F, which is the essential feature of the 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.

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First of all, we should understand that a function is the corresponding relationship between sets. Then, we should understand that there is more than one functional relationship between A and B, and finally we should focus on understanding the three elements of the function. The corresponding rules of functions are usually expressed by analytical expressions, but a large number of functional relationships can not be expressed by analytical expressions, but only by images, tables and other forms.