2022年人教A版数学必修一《第一章集合与《函数的概念》章节教案 .pdf

名师精编优秀教案湖北省武汉市蔡甸区第二中学高中数学人教版必修一第一章集合与函数的概念章节教案学习目标1.通过丰富实例，进一步体会函数是描述变量之间的依赖关系的重要数学模型，在此基础上学习用集合与对应的语言来刻画函数，体会对应关系在刻画函数概念中的作用；2.了解构成函数的要素；3.能够正确使用“区间”的符号表示某些集合.学习过程一、课前准备复习:（初中对函数的定义）在一个变化过程中，有两个变量x和y，对于x的的值，y 的值与之对应，此时y是x的函数，x是，y是 .表示方法有：、.二、新课导学学习探究探究任务一：函数 模型思想 及函数概念问题：研究下面三个实例：A.一枚炮弹发射，经26 秒后落地击中目标，射高为845 米，且炮弹距地面高度h（米）与时间t（秒）的变化规律是21305htt.B.近几十年，大气层中臭氧迅速减少，因而出现臭氧层空洞问题，图中曲线是南极上空臭氧层空洞面积的变化情况.C.国际上常用恩格尔系数（食物支出金额总支出金额）反映一个国家人民生活质量的高低.“八五”计划以来我们城镇居民的恩格尔系数如下表.讨论：以上三个实例存在哪些变量？变量的变化范围分别是什么？两个变量之间存在着这样的对应关系？三个 实例有什么共同点？新知：函数定义.设A、B是数集，如果，那么称:f AB 为从集合A到年份1991 1992 1993 1994 1995 恩格尔系数%53.8 52.9 50.1 49.9 49.9 名师精编优秀教案集合B的一个 函数，记作：(),yf xxA.其中，x叫，x的取值范围A叫作，与x的值对应的y值叫，函数值的集合()|f xxA 叫 .牛刀小试：函数223,1,0,1,2yxxx值域是 .反思：（1）值域与B的关系是；构成函数的三要素是、（2）常见函数的定义域与值域.探究任务二：区间及写法新知：设a、b是两个实数，且aa=、x|xb=、x|xb=.（2）|01x xx或=.（3）函数yx 的定义域，值域是 .（观察法）三、典型例题四、课堂练习1.已知函数2()21g tt，则(1)g（）.A.1 B.0 C.1 D.2 2.函数()12f xx 的定义域是（）.函数解析式定义域值域一次函数(0)yaxb a二次函数2yaxbx c，其中0a反比例函数(0)kykx文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 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D.1(,)23.已知函数()23f xx，若()1f a，则a=（）.A.2 B.1 C.1 D.2 4.函数2,2,1,0,1,2yxx的值域是 .5.函数2yx的定义域是，值域是 .（用区间表示）6.已知函数2()352f xxx，求(3)f、(2)f、(1)f a的值.7.求函数1()43f xx的定义域.8.已知函数1()1f xx.（1）求(3)f的值；（2）求函数的定义域（用区间表示）；（3）求2(1)f a的值.五、课堂小结学习小结函数模型应用思想；函数概念；二次函数的值域；区间表示.知识拓展求函数定义域的规则：分式：分母不等于0；偶次根式：根号里面大于或等于0；零次幂式：底数不等于0.文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 ZJ7B4I6C9W2文档编码:CC10J5U9Y4H9 HM1K6M6A5Y8 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