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1、單擊此處編輯母版標(biāo)題樣式,單擊此處編輯母版文本樣式,第二級(jí),第三級(jí),第四級(jí),第五級(jí),*,對(duì)數(shù)函數(shù)及其性質(zhì),一般地,如果,的,b,次冪等于,N,就是,,那么數(shù),b,叫做,以,a,為底,N,的,對(duì)數(shù),,記作,a,叫做對(duì)數(shù)的,底數(shù),,,N,叫做,真數(shù),。,定義,:,復(fù)習(xí)對(duì)數(shù)的概念,由前面的學(xué)習(xí)我們知道:有,一種細(xì)胞分裂時(shí),由,1,個(gè)分裂成,2,個(gè),,2,個(gè)分裂成,4,個(gè),, 1,個(gè)這樣的細(xì)胞分裂,x,次會(huì)得到多少個(gè)細(xì)胞?,如果知道了細(xì)胞的個(gè)數(shù),y,如何確定分裂的次數(shù),x,呢,由對(duì)數(shù)式與指數(shù)式的互化可知:,上式可以看作以,y,自變量的函數(shù)表達(dá)式嗎,?,對(duì)于每一個(gè)給定的,y,值都有惟一的,x,的值與之對(duì)
2、應(yīng),把,y,看作自變量,,x,就是,y,的函數(shù),但習(xí)慣上仍用,x,表示自變量,,y,表示它的函數(shù):即,這就是本節(jié)課要學(xué)習(xí)的:,定義:,函數(shù),,且,叫做,對(duì)數(shù)函數(shù),,其中,x,是自變量,函數(shù)的定義域是(,0,,,+,)。,對(duì)數(shù)函數(shù)及其性質(zhì),,,對(duì)數(shù)函數(shù),判斷:以下函數(shù)是對(duì)數(shù)函數(shù)的是 ( ),A. y=log,2,(3x-2) B. y=log,(x-1),x,C. y=log,1/3,x,2,D.y,=,lnx,E.,小試牛刀,D,二,.,對(duì)數(shù)函數(shù)的圖象,:,1.,描點(diǎn)畫圖,.,的變量,x,y,的對(duì)應(yīng)值對(duì)調(diào)即可得到,y=,log,a,x(a,0,且,a1),我們?nèi)『瘮?shù),注意只要把指數(shù)函數(shù),y=a
3、,x,(a0,且,a1),y=log x,和,y=log x,作圖,x,Y=log,2,x,1/8,1/4,1/2,1,2,4,8,-3,-2,-1,0,1,2,3,x,Y=log,1/2,x,-3,1/8,1/4,1/2,1,2,4,8,-2,-1,0,1,2,3,x,y,o,1 2 3 4 5 6 7 8,1,2,3,-1,-2,-3,Y=log,2,x,x,y,o,1 2 3 4 5 6 7 8,1,2,3,-1,-2,-3,Y=log,1/2,x,對(duì)數(shù)函數(shù)及其性質(zhì),探索研究:,在同一坐標(biāo)系中畫出下列對(duì)數(shù)函數(shù)的圖象;,(,1,),(,2,),(,3,),(,4,),. . . . . .
4、 . . . . .,. . . . . . . . . .,x,y,o,因?yàn)橹笖?shù)函數(shù),y=a,x,(0a1),與對(duì)數(shù)函數(shù),2.,利用對(duì)稱性畫圖,.,y=log,a,x(0adc,規(guī)律:在第一象限內(nèi),底數(shù)越大,圖像按順時(shí)針?lè)较蛐D(zhuǎn)。,一、對(duì)數(shù)函數(shù)的圖象與性質(zhì):,函數(shù),y = log,a,x ( a,0,且,a1 ),底數(shù),a 1,0 a 1,圖象,定義域,奇偶性,值域,定點(diǎn),單調(diào)性,函數(shù)值 符號(hào),1,x,y,o,1,x,y,o,非奇非偶函數(shù),非奇非偶函數(shù),( 0 , + ),R,( 1 , 0 ),即,x = 1,時(shí),,y = 0,在,( 0 , + ),上是增函數(shù),在,( 0 , + ),上
5、是減函數(shù),當(dāng),x,1,時(shí),,y,0,當(dāng),0,x,1,時(shí),,y,0,當(dāng),x,1,時(shí),,y,0,當(dāng),0,x,1,時(shí),,y,0,例,1:,求下列函數(shù)的定義域,:,(1) y=log,a,x,2,(2) y=log,a,(4-x),解,:,(1),因?yàn)?x,2,0,所以,x,即函數(shù),y=log,a,x,2,的定義域?yàn)?- ,(0,+,(2),因?yàn)?4-x0,所以,x0,因?yàn)?x-10,x-1,所以,1x0,log,0.5,(4x-3),0,x3/4,4x-3,定義域?yàn)?(3/4,1,1,、,2,、,3,、,4,、,例,2:,比較大小,對(duì)數(shù)函數(shù)及其性質(zhì),小結(jié),(,1,),本節(jié)要求掌握對(duì)數(shù)函數(shù)的概念、圖象和性質(zhì),(,2,)在理解對(duì)數(shù)函數(shù)的定義的基礎(chǔ)上,掌握對(duì)數(shù)函數(shù)的圖象和性質(zhì)的應(yīng)用是本小節(jié)的重點(diǎn),