函数创新题

• 机 构: 《数学金刊》试题研究组,
• 出 处: 数学教学通讯
• 发表日期: 2004年期
• 关键词: 二次函数 函数基 数形结合思想 分类讨论思想 函数问题 转化思想 奇偶性 判断函数 已知函数 恒成立

函数是高中数学学习的一条主线,其他知识或多或少都与其有关,其地位可见一斑.因此,它是高考考查的重点,占据着高考的半壁江山.每年全国各地的高考都会命制一些有关函数知识的创新试题,如以高等数学为背景定义新函数;与其他知识交汇设计试题,这种交汇在平时我们是很难遇到的,函数、导数、数列的交汇,函数、圆锥曲线、不等式的交汇等.为了让同学们能与函数创新题来一个亲密接触,本刊试题研究组的邵贤虎老师特意命制了五道颇有创意的试题.

Function is a main line of high school mathematics learning, other knowledge more or less related to its position can be seen.Therefore, it is the focus of college entrance examination, accounting for half of the college entrance examination.Every year the college entrance examination all over the country will order some of the relevant functions Innovative questions of knowledge, such as the definition of new functions in the context of advanced mathematics; intersection with other knowledge design questions, this intersection is usually difficult to meet, the intersection of function, derivative, sequence, function, conic, inequality Etc. In order to let the students can make a close contact with the function innovation, our teacher Shao Xianghu deliberately created five quite creative questions.