形如 y=x~α(常数α∈R)的函数叫做幂函数。课本只研究α为有理数的情形,并记成 y=x~n。当 n 取不同的有理数时,图象是怎样的形状,学生常感困惑。为了使学生能准确而迅速地画出幂函数的图象,我在教学中注意以函数性质作指导,从数量分析入手,逐步揭示图象特征;然后找出不同形状图象的数量界限,总结出一套易懂易记的画图规律。即:晓之以理,析之以数,表之以形,揭示规律。画幂函数图象的关键在于准确地判断其第一象限的图象。画第一象限图象可以函数的单调性、凹凸性的判定法以及互为反函数的图象关系作指导。 A function that is shaped like y=x~α (a constant α∈R) is called a power function. Textbooks only study cases where α is a rational number and are written as y=x~n. When n takes a different rational number, the shape of the image is, and students often feel puzzled. In order to enable students to draw power-function images accurately and quickly, I pay attention to the nature of functions as a guide in teaching, start with quantitative analysis, and gradually reveal the image features; then find out the boundaries of the number of different shape images, sum up A set of drawing rules that are easy to understand and easy to remember. That is: to understand the truth, to analyze the number, the form of the table to reveal the law. The key to drawing a power function image is to accurately determine the image of its first quadrant. Drawing the first quadrant image can be guided by the monotonicity of the function, the determination of the convexity and the image relationship of the inverse function.