對(duì)數(shù)函數(shù)的概念課件

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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),優(yōu)秀課件,*,對(duì)數(shù)函數(shù)的概念,1,優(yōu)秀課件,對(duì)數(shù)函數(shù)的概念1優(yōu)秀課件,復(fù)習(xí)回顧,換底公式,常用結(jié)論,2,優(yōu)秀課件,復(fù)習(xí)回顧換底公式常用結(jié)論2優(yōu)秀課件,在細(xì)胞分裂的問題中，細(xì)胞分裂個(gè)數(shù),y,和分裂次數(shù),x,的函數(shù)關(guān)系,用正整數(shù)指數(shù)函數(shù),y,=2,x,表示.在學(xué)習(xí)過程中我們已經(jīng)反它推廣到實(shí)數(shù)指數(shù)函數(shù).,分裂,?,次,細(xì)胞個(gè)數(shù),1萬,10萬,在,y,=2,x,中知,y,求,x,x,=log,2,y,3,優(yōu)秀課件,在細(xì)胞分裂的問題中，細(xì)胞分裂個(gè)數(shù)y和分裂次數(shù)x的函數(shù)關(guān)系,用,一般的指數(shù)函數(shù),y,=,a,x,(,a,0,

2、a,1),中的兩個(gè)變量,能不能把,y,當(dāng)作自變量,使得,x,是,y,的函數(shù)?,4,優(yōu)秀課件,一般的指數(shù)函數(shù)y=ax(a0,a1)中的兩個(gè)變量,能不能,對(duì)于任意,y,(0,+),有唯一,x,R,滿足,y,=,a,x,把,y,當(dāng)作,自變量,x,是,y,的函數(shù),x,=,log,a,y,(,a,0,a,1),x,1,x,2,y,2,y,1,x,y,y=a,x,(,a,1),x,1,x,2,y,1,y,2,y,=,a,x,(,a,0,a,1),對(duì)于,x,每一個(gè)確定值,y,都有唯一確定的值和它對(duì)應(yīng).,R,y|y0,一一對(duì)應(yīng),R,y|y0,5,優(yōu)秀課件,對(duì)于任意y(0,+)有唯一xR滿足y=ax把y當(dāng)作自變

3、,x,=,log,a,y,對(duì)數(shù)函數(shù),y,0,a,0,a,1,把函數(shù),y,=,log,a,x,(,a,0,a,1),叫作對(duì)數(shù)函數(shù),a,為對(duì)數(shù)函數(shù)的底數(shù),10為底的對(duì)數(shù)函數(shù),y,=,lg,x,為常用對(duì)數(shù)函數(shù),以無理數(shù)e,為底的對(duì)數(shù)函數(shù),y,=,ln,x,為自然對(duì),數(shù)函數(shù),6,優(yōu)秀課件,x=logay對(duì)數(shù)函數(shù)y0a0,a1把函數(shù)y=loga,【誤區(qū)警示】,本題易誤認(rèn)為,y,log,x,2,也是對(duì)數(shù)函數(shù)，錯(cuò)因在于對(duì)對(duì)數(shù)函數(shù)的概念理解不透徹；形如,y,log,a,x,(,a,0,，,a,1,，,x,0),的函數(shù)，才是對(duì)數(shù)函數(shù)，其中,x,在真數(shù)上，是自變量，,a,在底數(shù)上，是常數(shù),【思路點(diǎn)撥】,根據(jù)對(duì)數(shù)函

4、數(shù)的定義進(jìn)行判斷,例1.指出下列函數(shù)中哪些是對(duì)數(shù)函數(shù)：,(1),y,4,x,；,(2),y,log,x,2,；,(3),y,log,3,x,；,(4),y,log,0.4,x,；,(5),y,log,(2,a,1),x,(,a,1,2,且,a,1,；,(6),y,log,2,(,x,1),7,優(yōu)秀課件,【誤區(qū)警示】本題易誤認(rèn)為ylogx2也是對(duì)數(shù)函數(shù)，錯(cuò)因在,指數(shù)函數(shù),y,=,a,x,與對(duì)數(shù)函數(shù),x,=log,a,y,(,a,0,a,1)有什么關(guān)系?,函數(shù),自變量,因變量,定義域,值域,y,=,a,x,x,y,R,(0,+),x,=log,a,y,y,x,(0,+),R,稱這兩個(gè)函數(shù)互為,反函

5、數(shù),對(duì)應(yīng)關(guān)系互逆,指數(shù)函數(shù),y,=,a,x,是對(duì)數(shù)函數(shù),x,=log,a,y,(,a,0,a,1)的,反函數(shù),8,優(yōu)秀課件,指數(shù)函數(shù)y=ax與對(duì)數(shù)函數(shù)x=logay(a0,a1)有,指數(shù)函數(shù),y,=,a,x,(,a,0,a,1),對(duì)數(shù)函數(shù),y,=log,a,x,(,a,0,a,1),反函數(shù),互為反函數(shù),定義域和值域互換,對(duì)應(yīng)法則互逆,圖像關(guān)于直線,y=x,對(duì)稱,9,優(yōu)秀課件,指數(shù)函數(shù)y=ax(a0,a1)對(duì)數(shù)函數(shù)y=logax(a,例2 寫出下列對(duì)數(shù)函數(shù)的反函數(shù):,(1),y,=lg,x,;,(3),y=5,x,【點(diǎn)評(píng)】,解題時(shí)，求出反函數(shù)的解析式后，容易忽視標(biāo)明定義域，這一點(diǎn)一定要注意，通過

6、求出原來函數(shù)的值域來標(biāo)明反函數(shù)的定義域,10,優(yōu)秀課件,例2 寫出下列對(duì)數(shù)函數(shù)的反函數(shù):(3)y=5x 【點(diǎn)評(píng)】,提示：,(1),只有一一映射確定的函數(shù)才有反函數(shù),(2),求反函數(shù)的步驟可概括為一解、二換、三寫,(3),互為反函數(shù)的兩個(gè)函數(shù)，它們的圖像關(guān)于直線,y,x,對(duì)稱,(4),互為反函數(shù)的兩個(gè)函數(shù)的定義域與值域互換,(5),互為反函數(shù)的兩函數(shù)單調(diào)性一致,(6),奇函數(shù)的反函數(shù)仍是奇函數(shù)，偶函數(shù)無反函數(shù),如何理解反函數(shù)？,11,優(yōu)秀課件,提示：(1)只有一一映射確定的函數(shù)才有反函數(shù)如何理解反函數(shù),對(duì)數(shù)函數(shù)的定義域,求與對(duì)數(shù)函數(shù)有關(guān)的函數(shù)定義域時(shí)，除遵循前面已學(xué)習(xí)過的求函數(shù)定義域的方法外，還

7、要對(duì)對(duì)數(shù)函數(shù)自身有如下要求：一是要,注意真數(shù)大于零,；二是要,注意對(duì)數(shù)的底數(shù)大于零且不等于,1,.,12,優(yōu)秀課件,對(duì)數(shù)函數(shù)的定義域求與對(duì)數(shù)函數(shù)有關(guān)的函數(shù)定義域時(shí)，除遵循前面已,例3.求下列函數(shù)的定義域：,(1),y,log,a,(9,x,)(,a,0,，,a,1),；,(2),y,log,(,x,1),(3,x,),13,優(yōu)秀課件,例3.求下列函數(shù)的定義域：13優(yōu)秀課件,自我挑戰(zhàn),求下列函數(shù)的定義域：,(1),y,1,lg,(,x,1,),3,；,(2),y,log,x,(2,x,),14,優(yōu)秀課件,自我挑戰(zhàn) 求下列函數(shù)的定義域：(1)y1lg(x1),常見對(duì)數(shù)函數(shù)的圖像,15,優(yōu)秀課件,常

8、見對(duì)數(shù)函數(shù)的圖像15優(yōu)秀課件,【思路點(diǎn)撥】,采用列表描點(diǎn)法作出圖像，再討論它們的性質(zhì),例4.在同一坐標(biāo)系中畫出函數(shù),y,1,log,2,x,，,y,2,log,3,x,及,y,3,log,1,3,x,的圖像，并分析這些函數(shù),的性質(zhì),16,優(yōu)秀課件,【思路點(diǎn)撥】采用列表描點(diǎn)法作出圖像，再討論它們的性質(zhì)例4,【解】,(1),列表,17,優(yōu)秀課件,【解】(1)列表17優(yōu)秀課件,(2),描點(diǎn),(3),連線成圖,18,優(yōu)秀課件,(2)描點(diǎn)(3)連線成圖18優(yōu)秀課件,(4),性質(zhì)：,定義域,(0,，,),；,值域,R,；,y,1,log,2,x,，,y,2,log,3,x,在,(0,，,),上單調(diào)遞增,y,3,log,1,3,x,在,(0,，,),上單調(diào)遞減,此三個(gè)函數(shù),過定點(diǎn),(1,0),；,當(dāng),x,1,時(shí)，,y,1,0,，,y,2,0,，,y,3,0.,當(dāng),0,x,1,時(shí)，,y,1,0,，,y,2,0.,19,優(yōu)秀課件,(4)性質(zhì)：定義域(0，)；值域R；y1log,小結(jié),對(duì)數(shù)函數(shù)的概念,反函數(shù),定義域和值域互換,對(duì)應(yīng)關(guān)系互逆,y,=,log,a,x,(,a,0,a,1,x,0,),指數(shù)函數(shù),y,=,a,x,(,a,0,a,1)與對(duì)數(shù)函數(shù),y,=log,a,x,(,a,0,a,1),互為反函數(shù),20,優(yōu)秀課件,小結(jié)對(duì)數(shù)函數(shù)的概念反函數(shù)定義域和值域互換y=logax(a,