分段函数分段议 通情达意觅真谛

• 作 者: 冯玉翠
• 机 构: 乌海市滨河中学,
• 出 处: 中学时代
• 发表日期: 2012年14期
• 关键词: 分段函数 求值 图象解集 绝对值不等式 函数解析式 已知函数 二次函数 特殊值法 高考试题 奇偶性

初中阶段,通过观察一次、二次函数图象的变化情况,确定自变量的取值范围,然后分段求解析式,初中的分段函数多以直线型考查为主。高中阶段,从集合和对应关系角度引入函数,但分段函数在教材中是以例题的形式出现的,并未作深入说明。分段函数体现了“分类”的思想方法,解题突出分类,以分段函数为载体的问题时常在高考试题中“闪亮”登场。

In junior middle school, by observing the changes of primary and secondary function images, the range of independent variables is determined, and then the analytical expression is segmented. Most of the sub-functions in junior middle schools are mainly linear ones. In high school, the functions are introduced from the perspective of the collection and correspondence, but the segmentation function appears as an example in the textbook, which is not explained in depth. Segmentation function reflects the “category ” way of thinking, problem-solving highlight the classification, the function of the segmented function as a carrier often in the entrance examination questions “shiny ” debut.