Power functions, exponential functions, logarithmic functions, trigonometric functions and inverse trigonometric functions are the five basic elementary functions. Since we have already studied these functions in depth in middle school mathematics, we will only briefly review them here.

　　Generally, we take the form

,

The function of is called a power function, where  is the independent variable and  is a constant. Its domain depends on what number  is. ,  ,  ,  ,  , it is the most commonly used power function. Its images are shown in the following figures (a), (b), (c) .

        Graphical animation of  power function :

1. [ animation ]; 2. [ animation ].

　　Attached below is a summary of the properties of power functions learned in middle school .

　　Properties of power functions:
　　(1) All power functions are defined on , and the graphs pass through the point ;
　　(2) If , the graph of the power function passes through the origin, and the function increases monotonically on the interval ;
　　(3) If , the power function is a monotonically decreasing function on the interval . In the first quadrant, when the independent variable approaches the origin from the right, the image infinitely approaches the axis from the right of the axis. When tending to , the image approaches -axis infinitely from above the axis ;
　　(4) When is an odd number, the power function is an odd function ; when is an even number, the power function is an even function .

　　Image characteristics of power function: