必修1单调性与奇偶性复习

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1、 学生教案教师姓名学生姓名 填写时间2014-1-1年级高一学科数学上课时间2014-1-1 08:00-10:00阶段基础（ ） 提高（）强化（ ）课时计划第（ ）次课共（ ）次课教学目标1、 掌握函数的单调性、奇偶性的基本性质；2、 熟悉如何求单调区间、最值问题；3、 根据单调性、奇偶性的基本性质解题；重难点1、 掌握函数的最值的求值；2、 单调性与奇偶性的综合解题。 课后作业：教师评语及建议：科组长签字：函数的单调性 增（减）函数： 一般地，设函数的定义域为，区间如果对于区间内的任意两个值，当时，都有 ，那么就说在区间上是单调增（减）函数，称为的单调增（减）区间注意：“任意”、“都有”等

2、关键词；. 单调性、单调区间是有区别的；单调性：如果函数y=f(x)在某个区间上是增函数或是减函数，那么就说函数y=f(x)在这一区间具有（严格的）单调性，区间D叫做y=f(x)的单调区间：* 注意判断函数单调性的步骤利用定义证明函数f(x)在给定的区间D上的单调性的一般步骤： 任取x1，x2D，且x1x2； 作差f(x1)f(x2)；变形（通常是因式分解和配方）；定号（即判断差f(x1)f(x2)的正负）；下结论（即指出函数f(x)在给定的区间D上的单调性）* 复合函数的单调性判断.以复合函数为例.可按下列步骤操作.1. 将复合函数分解成基本初等函数： ,：2. 分别确定各个函数的定义域3.

3、 分别确定分解成的两个基本初等函数的单调区间4. 若两个基本初等函数单调性性相同,则复合函数单调递增,否则相反.考点分析：1、点调性的理解例1、函数y=x2-6x的减区间是 变式1、函数的y=-2x2+3x+1，0,2减区间是 ，增区间是 。2、函数单调性的证明例1、：证明函数在上是减函数。变式1、：求证：在区间上是减函例3：函数的单调增区间为（ ）ABCD变式1：函数在定义域上的单调性为( )（A）在上是增函数，在上是增函数; （B）减函数;（C）在上是减函数，在上是减函数; （D）增函数2、函数单调性的应用（判断值的大小，求最值、值域，注意二次函数）例：已知定义域在-1,2函数，则该函数的

4、值域为_.变式：函数在1,3上的最大值为_.变式：函数在-2,3上的最小值为_.变式：已知函数f(x)在区间上是减函数,则与的大小关系是 函数的奇偶性1、奇函数与偶函数的概念 偶函数：一般地，对于函数定义域内的任意一个x，都有，那么函数叫偶函数。奇函数：一般地，对于函数定义域内的任意一个x，都有，那么函数叫奇函数。（如果函数是奇函数或偶函数，则称这个函数具有奇偶性。）2、奇函数与偶函数的特征 * 定义域关于原点对称； * 奇函数图象关于原点对称；且当函数在x=0处有意义时，； * 偶函数图象关于y轴对称。3、函数奇偶性的证明方法：判断定义域是否关于原点对称； 判断与的关系。考点分析：1、函数奇

5、偶性的判断（先判断定义域）例1、：判断下列函数的奇偶性。（1）； （2）.变式1：有4个函数：，其中偶函数的个数是（ ）（） （）（）（）变式2：下列函数为偶函数的是（ ）A B C D.例2，判断下列函数的奇偶性：例3：设f(x)的定义域为R的函数,求证: 是偶函数； 是奇函数.分析：函数奇偶性的判断：（1）定义域关于原点对称；（2）.变式1. 已知f(x)是奇函数，g(x)是偶函数，求函数f(x)g(x)的奇偶性。变式2. 已知函数为奇函数，为偶函数,且，求与.3、 函数奇偶性的应用例1、：已知 是定义在上的奇函数，当时， 的图象如右图所示，那么f (x) 的值域是 .变式1：设f(x)a

6、xbx5，已知f(7)17,求f(7)的值。变式2、（1）已知函数，求的值. （2）已知函数若，求的值。例2、：已知函数是奇函数，当时，；则当时，= .O变式1、：已知函数是定义在R上的奇函数，当x0时，图象如图所示（1）画出当0时的图象（2）求出函数的解析式（要求写出求解过程）单调性与奇偶性的综合应用例1、：若奇函数f (x) 在3，7上是增函数且最小值为5，求f (x) 在7，3上的单调性和最值。 例2、：定义在上的奇函数在整个定义域上是减函数，若，求实数的取值范围；变式1：已知f (x)为定义在-1,1上的奇函数，且f (x)在定义域上单调递减，0，求a的取值范围。变式2、若偶函数在上是

7、增函数，则下列关系式中成立的是（ ）A B C D 单调性奇偶性课后习题1.已知函数 f(x)为偶函数，在（0,+上为减函数，若f(0f()，则方程f(x)0的根的个数是 （ ）A 2 B 2或1 C 3 D 2或32.设是R上的减函数，则下列关系成立的是（ ） A、B、C、D、3.如果奇函数在区间上是增函数，且最小值为，那么 在区间上是（ ） A、增函数且最小值为B、增函数且最大值为C、减函数且最小值为D、减函数且最大值为4、在区间上不是增函数的是（ ）A B C D5、设函数f(x)是R上的偶函数，且在上是减函数，若且，则A、 B、 C、 D、不能确定6、如果函数f(x)x2(a-1)x2

8、在区间（，4上是减函数，则实数a的取值范围是 （ ）A. B. C. D. 7、设定义在上的偶函数在区间上单调递减，若 ，实数的取值范围是_8、下列命题中不正确的是_（填上所有不正确命题的序号）因为函数分别在内都是减函数，所以函数在整个定义域内是单调递减的。函数在上是减函数。有些函数没有单调区间，或者它的定义域根本就不是区间。9.求下列函数的单调区间（1）y（2）（3）10.定义在R上的函数，当时，且对任意的，有（1）证明：；（2）证明：对任意的，恒有；（3）证明是R上的增函数；（4）若，求的取值范围11、设的定义域为，且在上为增函数，（1）求证；（2）设，解不等式12、已知函数f(x)是定义

9、在R上的增函数，设F(x)=f(x)-f(a-x),试用函数单调性的定义证明F（x）是R上的增函数 tomorrow I go fishing to the East. Bosses dont have fish to eat. Positions out of a fat man: going on now in the past, the Imperial Army came after eating is bad. Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen

10、said: I think so well! Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: old Kings Head tomorrow, your fish such as we Captain! Know this is the Kings voice, by far. At night, the ship to port, n

11、ext to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Dev

12、ils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, dont know direction, and had to let the old K

13、ing was driving. Old King pulling two oars said: good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. No, the cabin there was grunting . Shout . snore. The next morning, Miaogang the Lion Bridge a mourning fishermans woman. Head wrapped in white cloth, foot-wear w

14、hite shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West,

15、 there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearm

16、s, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight

17、rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China peoples armed f

18、orces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Governments traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermens uncle

19、 Wangs boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch . Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on.

20、 Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: Mister lucky, MA Yang, this is net live fish, Fu shengs brother to try it. The elves called Fu sheng came holding a fish said: old Kings Head, today luck was not bad! Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. That is a shame