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幂函数是高中数学的一个内容,也是函数的重要模型,如何很好地掌握幂函数的图像和性质呢?首先要识记幂函数在第一象限内的图像,其次分析幂函数的奇偶性,得出整个幂函数的图像与性质.幂函数y=xα在第一象限的图像如图1所示,图像恒过(1,1).幂指数α>0时,图像过点(0,0),为增函数,其中0<α<1,函数图像上凸递增;α>1,函数图像下凸递增;α=0时为直线y=1(除去点(0,1));α<0时为减函数.
Power function is a high school mathematics content, but also an important model of the function, how to master the image and the nature of the power function? First of all, to recognize the power function in the first quadrant of the image, followed by analysis of the parity of the power function, Get the image of the power function and the nature of the power function y = xα in the first quadrant of the image shown in Figure 1, the image is always over (1,1) .If the power exponent α> 0, the image is too point (0,0 ) Is an increasing function, where 0 <α <1, convexity increases on the function image; α> 1, the convex image of the function increases incrementally; when α = 0, 0 for the reduced function.