1, the traditional definition of function: suppose there are two variables X and Y in a certain change process, and if Y has a unique definite value corresponding to each definite value of X in a certain range, then Y is said to be a function of X, and X is called an independent variable.

2. Modern definition of function: Let A and B be sets of non-empty numbers, and f:x→y is a corresponding rule from A to B, then the mapping f:A→B from A to B is called a function, denoted as y = f(x), where x∈A, y∈B, and the original image set A is called function f(x

Properties of functions

1, symmetry

Number axis symmetry: the so-called number axis symmetry means that the function image is symmetrical about the coordinate axes X and Y..

Symmetry of origin: Similarly, such symmetry means that the image is symmetrical about the origin, and the coordinate values of the points on the function with the same distance from the origin on both sides of the origin are opposite to each other.

About point symmetry: this type is quite similar to the origin symmetry, but the difference is that the symmetry point is no longer limited to the origin, but any point on the coordinate axis.

2. periodicity

The images of functions appear repeatedly in some areas. Assuming that a function F(X) is a periodic function, there is a real number T. When all the X in the definition domain are added or subtracted by integer multiples of T, the Y corresponding to X remains unchanged, so it can be said that T is the period of the function. If the absolute value of T reaches the minimum, it is called the minimum period.