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近几年数学中考中屡屡见到一些双反比例函数图象、面积问题,本文拟探究此类问题中基本图形的一般规律,以供大家参考.如图1,点B是反比例函数y=k_1/x图象上的任意一点,过点B分别向x轴、y轴作垂线,垂足为A、B,与反比例函数y=k_2/x的图象交于点E、F.为了问题研究的方便,不妨规定k_1>k_2>0,且仅研究第一象限内函数图象问题.(若无特别说明,下同)结论 1四边形EOFB的面积为k_1-k_2.证明由反比例函数的面积性质,可知
In recent years, mathematics senior high school entrance examination often see some double inverse proportion function images, area problems, this article to explore the general laws of such graphics in the basic graphics for your reference.As shown in Figure 1, B is the inverse proportion function y = k_1 / At any point on the x-image, point B is perpendicular to the x-axis and the y-axis, respectively. The footings are A and B, and the image with the inverse proportion function y = k_2 / x is placed at points E and F. For the sake of research , We may consider that k_1> k_2> 0, and only study the problem of the functional image in the first quadrant. (Unless otherwise stated, the same below) Conclusion 1 The area of the quadrilateral EOFB is k_1-k_2. , We can see