In mathematics, the graph (or image) of function F refers to the set composed of all ordered number pairs (x, f(x)). Specifically, if x is a real number, then the function graph is represented as a curve in the plane rectangular coordinate system.

If the function independent variable x is an ordered pair of two real numbers (x 1,? X2), then this graph is all third-order (x 1,? x2，？ f(x 1，？ X2)), presented as a curved surface (see 3D computer graphics).

German mathematician Riemann introduced a new definition of function: "For every value of X, Y always has a completely certain value corresponding to it. No matter what method is used to establish the corresponding relationship between X and Y, Y is called the function of X."

From the evolution of the concept of function above, we can know that the definition of function must grasp the essential attributes of function. The variable y is called a function of x, and there is only one law, so that every value in the range of this function has a certain Y value corresponding to it, no matter whether this law is a formula, an image, a table or other forms.

Thus, there is the definition of function in our textbook: generally speaking, if there are two variables X and Y in a change process, and for each certain value of X, Y has a unique definite value corresponding to it, then we say that X is an independent variable and Y is a function of X.