幂函数习题精选精讲The power function exercises featured Jingjiang .doc

幂函数习题精选精讲1（The power function exercises featured Jingjiang 1） power function As the main function of high school mathematics, throughout the high school mathematics learning always, and the power function is a part of which, though it simple, but contains some important mathematical ideas. The analysis of several cases, in order to expand students thinking. First, classification discussion thought Image 1 cases of known functions with two axes have no common points, and the image on the Y axis, and N values, and draw the function of the image. Solution: because the image and Y axis without public, therefore, and image symmetry on the Y axis, it is even, by, too, because, so. At that time, not even; At that time, even; At that time, even; At that time, not even; At that time, even; So n is 1 or 3.. At this time, analytical power function or its image, as shown in Figure 1. Two, combined with the number and shape of thought 2 cases of known points in the image of the power function, power function, in the image. When asked why the X values are: (1); (2); (3). Analysis: from the definition of power function, first calculate the analytic formula and the reuse of image judgment. Solution: set by you to, So, that is. Then by order, you have to, So, that is made. In the same coordinate system With the image, as shown in Figure 2 by the image: (1) when or when,; (2) at the time,; (3) if and when. Summary: the combination has important applications in inequality, pay attention to the implied conditions. Three, the transformation of mathematical thinking 3 cases of domain function is all real, then the range of real m is (). A. B. C. D. Analysis: to make the domain of the function is all real, can be transformed into are established for all that is real. The solution (B). The power function of three kinds of questions The so-called classification discussion, the essence is to crush one by one, break up the whole into parts, zero for the whole plot strategy. Classification dis