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如果能迅速画出函数图象的示意图,便能直观清楚地看出函数的性质,从而提高解题能力,但幂函数y=x~2的图象不如其他函数那样定型,只要指数n稍有不同,图象的形状可能大大不同,鉴于此,在教学中我引导学生探索规律,抓住关键,突破难点,总结出了利用四个特殊点和一句口诀画幂函数图象示意图的方法,使用起来简便有效。 Ⅰ、四个特殊点:(1,1)、(0,0)、(—1.1)和(—1,—1),由是否经过这四个特殊点可确定幂函数图象的位置和对称性。 Ⅱ、一句口诀:在(0.1)区间.越小越上(指数小的图象在上)。 关于Ⅰ说明如下: 这里只研究n是非零有理数的情况,不妨设n—p/q(p、q是非零整数,且|p|与|q|互质)。
If you can quickly draw a schematic diagram of the function image, you can intuitively and clearly see the nature of the function, thereby increasing the ability to solve problems, but the power function y = x ~ 2 image is not fixed as other functions, as long as the index n slightly Differently, the shape of the image may be greatly different. In view of this, in the teaching, I guide the students to explore the law, grasp the key, break through the difficulties, and sum up the method of using four special points and a mouthful to draw a power function image. It is simple and effective. I. Four special points: (1,1), (0,0), (-1.1), and (—1, -1). The position and symmetry of the power function image can be determined by passing through these four special points. Sex. II. A word of mouth: in the (0.1) interval, the smaller the number is, the smaller (the smaller the index is on the top). About I description is as follows: Here only study the case of n is a non-zero rational number, may wish to set n-p / q (p, q is a non-zero integer, and | p | and | q | relatively prime).