Power function is a common function in mathematics, and its function expression is like y = x n, where n is a real number and not zero. The following will analyze nine basic images of power function.
1, when n >; 0, the power function increases. When x gradually increases, the corresponding y value will also increase. In this case, the power function image shows the characteristics of rising gradually from the lower left to the upper right.
2. when n
3. When n= 1, the image of function y=x is a straight line with a slope of 1, which passes through the origin and gradually rises from bottom left to top right.
4. When n=- 1, the image of function y= 1/x is a hyperbola, which moves from the second quadrant to the first quadrant and then approaches the X axis through the origin, and gradually descends from the upper left to the lower right.
5. When-1
6. When n >; At 1, the image with function y=x n is steeper than the image with function y=x, and the corresponding y value increases faster when x increases gradually.
7. when n
8. When n=0, the image of function y = x 0 is a horizontal straight line y= 1, which is parallel to the X axis.
9. when x
abstract
By analyzing the values of different parameters n of power function, nine basic images of power function can be obtained. These images show the increase, decrease and horizontal straight line of power function, which can help us better understand and analyze the nature and behavior of power function.