最新3[1].高一数学人教新课标A版函数及其表示方法教案!+2名师优秀教案.doc
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1、31.高一数学(人教新课标A版)函数及其表示方法教案! 2函数及其表示方法 一、目标认知 学习目标: (1)会用集合与对应的语言刻画函数;会求一些简单函数的定义域和值域,初步掌握换元法的简单运用. (2)能正确认识和使用函数的三种表示法:解析法,列表法和图象法(了解每种方法的优点(在实际情 境中,会根据不同的需要选择恰当的方法表示函数; (3)求简单分段函数的解析式;了解分段函数及其简单应用( 重点: 函数概念的理解,函数关系的三种表示方法(分段函数解析式的求法( 难点: 对函数符号的理解;对于具体问题能灵活运用这三种表示方法中的某种进行分析,什么才算“恰当”,分段函数解析式的求法( 二、知识
2、要点梳理 知识点一、函数的概念 1(函数的定义 设A、B是非空的数集,如果按照某个确定的对应关系f,使对于集合A中的任意一个数x,在集合B中都有唯一确定的数f(x)和它对应,那么就称f:A?B为从集合A到集合B的一个函数. 记作:y=f(x),xA( 其中,x叫做自变量,x的取值范围A叫做函数的定义域;与x的值相对应的y值叫做函数值,函数值的集合f(x)|xA叫做函数的值域. 2(构成函数的三要素:定义域、对应关系和值域 ?构成函数的三个要素是定义域、对应关系和值域.由于值域是由定义域和对应关系决定的,所以,如果两个函数的定义域和对应关系完全致,即称这两个函数相等(或为同一函数); ?两个函数
3、相等当且仅当它们的定义域和对应关系完全致,而与表示自变量和函数值的字母无关. 3(区间的概念 (1)区间的分类:开区间、闭区间、半开半闭区间; (2)无穷区间; (3)区间的数轴表示( 区间表示: x|a?x?b=a,b; ; ; anti-Japanese patriotism. Under the influence of the party, Zhu, Wang, acting in strict discipline, political, military quality and combat effectiveness has improved. As well as youth
4、service corps, womens service and young pioneers, countryside-Japanese performance, posting anti-Japanese slogans, operate private schools, literacy classes, founder of the iron, and the tongue and the sound, sparks and other anti-Japanese mimeographed tabloid, actively promote anti-Japanese. Hancha
5、ng recovery after the party, that is, Jiangnan anti-Japanese guerrilla people save, Shen Yingjie, Xu Azhen to participate in development of the Chinese Communist Party, in October and set up a water party group in Hong Kong, Han chang long party group. Meanwhile, Xu on cleaning two wannan, demanding
6、 new army deployed cadres, and have sent many new progressive youth to receive training. On November 9, sheng, Wu Xing, Nanxun, jiaxing, Tongxiang, Zonta, Hangzhou, wukang strongholds such as Elves, nearly all men, together with the aircraft, boats, Zhu Xi Lu, pouncing on troop locations. 10th, the
7、enemies have invaded yan Tomb, Xin Cheng, Wuzhen. 11th, Zhu Xi army pier at Bell House was surrounded by the enemy, break, casualties will be great, CPC party member Xu, Xu Quansheng, really so magnificent and head of three Wang Yulin, also died in the battle. Zhu Xi withdrew the remnants of more th
8、an 400 people back to Xiao Feng integration. Jie Xu with the new cadres, Communist party Mr CHOW (Zhou kangyu) came from southern Anhui. Zhu Xi Wei CHOY for staff officers. The end of unified leadership . 知识点二、函数的表示法 1(函数的三种表示方法: 解析法:用数学表达式表示两个变量之间的对应关系( 优点:简明,给自变量求函数值. 图象法:用图象表示两个变量之间的对应关系( 优点:直观形象
9、,反应变化趋势. 列表法:列出表格来表示两个变量之间的对应关系( 优点:不需计算就可看出函数值. 2(分段函数: 分段函数的解析式不能写成几个不同的方程,而应写函数几种不同的表达式并用个左大括号括起来,并分别注明各部分的自变量的取值情况( 知识点三、映射与函数 1.映射定义: 设A、B是两个非空集合,如果按照某个对应法则f,对于集合A中的任何一个元素,在集合B中都有唯一的元素和它对应,这样的对应叫做从A到B的映射;记为f:A?B. 象与原象:如果给定一个从集合A到集合B的映射,那么A中的元素a对应的B中的元素b叫做a的象,a叫做b的原象. 注意: (1)A中的每一个元素都有象,且唯一; (2)
10、B中的元素未必有原象,即使有,也未必唯一; (3)a的象记为f(a). 2.函数: 设A、B是两个非空数集,若f:A?B是从集合A到集合B的映射,这个映射叫做从集合A到集合B的函数,记为y=f(x). 注意: (1)函数一定是映射,映射不一定是函数; (2)函数三要素:定义域、值域、对应法则; (3)B中的元素未必有原象,即使有原象,也未必唯一; (4)原象集合=定义域,值域=象集合. 三、规律方法指导 1.函数定义域的求法 (1)当函数是以解析式的形式给出时,其定义域就是使函数解析式有意义的自变量的取值的集合.具体地讲,就是考虑分母不为零,偶次根号的被开方数、式大于或等于零,零次幂的底数不为
11、零以及我们在后面学习时碰到的所有有意义的限制条件. (2)当函数是由实际问题给出时,其定义域不仅要考虑使其解析式有意义,还要有实际意义. (3)求函数的定义域,一般是转化为解不等式或不等式组的问题,注意定义域是一个集合,其结果必须用集合或区间来表示. 2.如何确定象与原象 anti-Japanese patriotism. Under the influence of the party, Zhu, Wang, acting in strict discipline, political, military quality and combat effectiveness has improv
12、ed. As well as youth service corps, womens service and young pioneers, countryside-Japanese performance, posting anti-Japanese slogans, operate private schools, literacy classes, founder of the iron, and the tongue and the sound, sparks and other anti-Japanese mimeographed tabloid, actively promote
13、anti-Japanese. Hanchang recovery after the party, that is, Jiangnan anti-Japanese guerrilla people save, Shen Yingjie, Xu Azhen to participate in development of the Chinese Communist Party, in October and set up a water party group in Hong Kong, Han chang long party group. Meanwhile, Xu on cleaning
14、two wannan, demanding new army deployed cadres, and have sent many new progressive youth to receive training. On November 9, sheng, Wu Xing, Nanxun, jiaxing, Tongxiang, Zonta, Hangzhou, wukang strongholds such as Elves, nearly all men, together with the aircraft, boats, Zhu Xi Lu, pouncing on troop
15、locations. 10th, the enemies have invaded yan Tomb, Xin Cheng, Wuzhen. 11th, Zhu Xi army pier at Bell House was surrounded by the enemy, break, casualties will be great, CPC party member Xu, Xu Quansheng, really so magnificent and head of three Wang Yulin, also died in the battle. Zhu Xi withdrew th
16、e remnants of more than 400 people back to Xiao Feng integration. Jie Xu with the new cadres, Communist party Mr CHOW (Zhou kangyu) came from southern Anhui. Zhu Xi Wei CHOY for staff officers. The end of unified leadership 对于给出原象要求象的问题,只需将原象代入对应关系中,即可求出象.对于给出象,要求原象的问题,可先假设原象,再代入对应关系中得已知的象,从而求出原象;也可
17、根据对应关系,由象逆推出原象. 3.函数值域的求法 实际上求函数的值域是个比较复杂的问题,虽然给定了函数的定义域及其对应法则以后,值域就完全确定了,但求值域还是特别要注意讲究方法,常用的方法有: 观察法:通过对函数解析式的简单变形,利用熟知的基本函数的值域,或利用函数的图象的最高点和最低点,观察求得函数的值域; 配方法:对二次函数型的解析式可先进行配方,在充分注意到自变量取值范围的情况下,利用求二次函数的值域方法求函数的值域; 判别式法:将函数视为关于自变量的二次方程,利用判别式求函数值的范围,常用于一些分式函数等;此外,使用此方法要特别注意自变量的取值范围; 换元法:通过对函数的解析式进行适
18、当换元,将复杂的函数化归为几个简单的函数,从而利用基本函数的取值范围来求函数的值域. 求函数的值域没有通用的方法和固定的模式,除了上述常用方法外,还有最值法、数形结合法等.总之,求函数的值域关键是重视对应法则的作用,还要特别注意定义域对值域的制约. 经典例题透析 类型一、函数概念 1.下列各组函数是否表示同一个函数, (1) (2) (3) (4) 思路点拨:对于根式、分式、绝对值式,要先化简再判断,在化简时要注意等价变形,否则等号不成立. 解:(1),对应关系不同,因此是不同的函数; (2)的定义域不同,因此是不同的函数; (3)的定义域相同,对应关系相同,因此是相同的函数; (4)定义域相
19、同,对应关系相同,自变量用不同字面表示,仍为同一函数. anti-Japanese patriotism. Under the influence of the party, Zhu, Wang, acting in strict discipline, political, military quality and combat effectiveness has improved. As well as youth service corps, womens service and young pioneers, countryside-Japanese performance, post
20、ing anti-Japanese slogans, operate private schools, literacy classes, founder of the iron, and the tongue and the sound, sparks and other anti-Japanese mimeographed tabloid, actively promote anti-Japanese. Hanchang recovery after the party, that is, Jiangnan anti-Japanese guerrilla people save, Shen
21、 Yingjie, Xu Azhen to participate in development of the Chinese Communist Party, in October and set up a water party group in Hong Kong, Han chang long party group. Meanwhile, Xu on cleaning two wannan, demanding new army deployed cadres, and have sent many new progressive youth to receive training.
22、 On November 9, sheng, Wu Xing, Nanxun, jiaxing, Tongxiang, Zonta, Hangzhou, wukang strongholds such as Elves, nearly all men, together with the aircraft, boats, Zhu Xi Lu, pouncing on troop locations. 10th, the enemies have invaded yan Tomb, Xin Cheng, Wuzhen. 11th, Zhu Xi army pier at Bell House w
23、as surrounded by the enemy, break, casualties will be great, CPC party member Xu, Xu Quansheng, really so magnificent and head of three Wang Yulin, also died in the battle. Zhu Xi withdrew the remnants of more than 400 people back to Xiao Feng integration. Jie Xu with the new cadres, Communist party
24、 Mr CHOW (Zhou kangyu) came from southern Anhui. Zhu Xi Wei CHOY for staff officers. The end of unified leadership 总结升华:函数概念含有三个要素,即定义域,值域和对应法则,其中核心是对应法则,它是函数关系的本质特征.只有当两个函数的定义域和对应法则都分别相同时,这两个函数才是同一函数,换言之就是: (1)定义域不同,两个函数也就不同; (2)对应法则不同,两个函数也是不同的. (3)即使定义域和值域都分别相同的两个函数,它们也不一定是同一函数,因为函数的定义域和值域不能唯一地确定
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