Power function is one of the basic elementary functions. Generally speaking, the function of y=xα(α is rational number), that is, the function with base as independent variable, power as dependent variable and exponent as constant is called power function. Such as function y=x0? , y=x 1, y=x2, y=x- 1 (note: y = x-1=1x, x≠0 when y=x0) and so on are all power functions.

Extended data:

First, the positive nature.

When α >; 0, the power function y=xα has the following properties:

A, the images all pass through the point (1,1) (0,0);

B, the function in the image is the increasing function in the interval [0, +∞);

C, in the first quadrant, α >; 1, the derivative value increases gradually; When α= 1, the derivative is constant; 0 & ltα& lt； 1, the derivative value gradually decreases and approaches 0 (the function value increases);

Second, negativity.

When α

A, the images all pass through the point (1,1);

B, the image is a decreasing function in the interval (0, +∞); (Content supplement: If it is X-2, it is easy to get that it is an even function. Using symmetry, the symmetry axis is the Y axis, and the image can be monotonically increased in the interval (-∞, 0). The same is true for other even functions).

C, in the first quadrant, there are two asymptotes (coordinate axes), the independent variable approaches 0, the function value approaches +∞, the independent variable approaches +∞, and the function value approaches 0.