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数形结合思想的实质即通过数与形之间的相互转化,把抽象的数量关系,转化为适当的图形,从图形的结构直观地发现数量之间存在的内在联系,解决数量关系的数学问题.如何让解决问题的方法进一步提炼成简单易懂的、直观的形式呢?这就要求结合数、形、图来分析.一、数形结合在数与式中的应用例1.求|x-1|+|x-2|+|x-3|的最小值.分析:绝对值可以通过数轴这个工具与两点间
The essence of the combination of numbers and figures is the conversion of the abstract quantitative relations into the appropriate figures through the mutual transformation of numbers and forms, the direct finding of the intrinsic relations between the quantities from the structure of the figures and the mathematical problems of solving the quantitative relations How to solve the problem of the method further refined into easy to understand, intuitive form? This requires the combination of number, shape, figure to analyze. -1 | + | x-2 | + | x-3 | Analysis: The absolute value can be calculated by the number of axes between this tool and two points