對(duì)數(shù)函數(shù)的概念課件

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=2x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=2x中知y求xx=log2y3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=ax(a>0,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(a>0,a≠1)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=ax把y當(dāng)作自變量,x是y的函數(shù)x=logay(a>0,a≠1)x1x2y2y1xyy=ax(a>1)x1≠x2y1≠y2y=ax(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|y>0}一一對(duì)應(yīng)R{y|y>0}5優(yōu)秀課件對(duì)于任意y∈(0,+∞)有唯一x∈R滿足y=ax把y當(dāng)作自變x=logay對(duì)數(shù)函數(shù)y>0a>0,a≠1把函數(shù)y=logax(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=lgx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=lnx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)y>0a>0,a≠1把函數(shù)y=loga【誤區(qū)警示】本題易誤認(rèn)為y＝logx2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＝logax(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＝4x；(2)y＝logx2；(3)y＝－log3x；

(4)y＝log0.4x；(5)y＝log(2a－1)x(a>12且a≠1；

(6)y＝log2(x＋1)．

7優(yōu)秀課件【誤區(qū)警示】本題易誤認(rèn)為y＝logx2也是對(duì)數(shù)函數(shù)，錯(cuò)因在指數(shù)函數(shù)y=ax與對(duì)數(shù)函數(shù)x=logay(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=axxyR(0,+∞)x=logayyx(0,+∞)R稱這兩個(gè)函數(shù)互為反函數(shù)對(duì)應(yīng)關(guān)系互逆指數(shù)函數(shù)y=ax是對(duì)數(shù)函數(shù)x=logay(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(a>0,a≠1)有指數(shù)函數(shù)y=ax(a>0,a≠1)對(duì)數(shù)函數(shù)y=logax(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(a>0,a≠1)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=lgx;

(3)y=5x

【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＝loga(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＝1lg(x＋1)－3；

(2)y＝logx(2－x)．

14優(yōu)秀課件自我挑戰(zhàn)求下列函數(shù)的定義域：(1)y＝1lg(x＋1)－常見對(duì)數(shù)函數(shù)的圖像15優(yōu)秀課件常見對(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)y1＝log2x，y2＝log3x及y3＝log13x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)：①定義域(0，＋∞)；②值域R；③y1＝log2x，y2＝log3x在(0，＋∞)上單調(diào)遞增．y3＝log13x在(0，＋∞)上單調(diào)遞減．④此三個(gè)函數(shù)過定點(diǎn)(1,0)；⑤當(dāng)x>1時(shí)，y1>0，y2>0，y3<0.當(dāng)0<x<1時(shí)，y1<0，y2<0，y3>0.

19優(yōu)秀課件(4)性質(zhì)：①定義域(0，＋∞)；②值域R；③y1＝log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=logax(a>0,a≠1,x>0)指數(shù)函數(shù)y=ax(a>0,a≠1)與對(duì)數(shù)函數(shù)y=logax(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>對(duì)數(shù)函數(shù)的概念21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22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=2x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=2x中知y求xx=log2y23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=ax(a>0,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)?24優(yōu)秀課件一般的指數(shù)函數(shù)y=ax(a>0,a≠1)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=ax把y當(dāng)作自變量,x是y的函數(shù)x=logay(a>0,a≠1)x1x2y2y1xyy=ax(a>1)x1≠x2y1≠y2y=ax(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|y>0}一一對(duì)應(yīng)R{y|y>0}25優(yōu)秀課件對(duì)于任意y∈(0,+∞)有唯一x∈R滿足y=ax把y當(dāng)作自變x=logay對(duì)數(shù)函數(shù)y>0a>0,a≠1把函數(shù)y=logax(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=lgx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=lnx為自然對(duì)數(shù)函數(shù)26優(yōu)秀課件x=logay對(duì)數(shù)函數(shù)y>0a>0,a≠1把函數(shù)y=loga【誤區(qū)警示】本題易誤認(rèn)為y＝logx2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＝logax(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＝4x；(2)y＝logx2；(3)y＝－log3x；

(4)y＝log0.4x；(5)y＝log(2a－1)x(a>12且a≠1；

(6)y＝log2(x＋1)．

27優(yōu)秀課件【誤區(qū)警示】本題易誤認(rèn)為y＝logx2也是對(duì)數(shù)函數(shù)，錯(cuò)因在指數(shù)函數(shù)y=ax與對(duì)數(shù)函數(shù)x=logay(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=axxyR(0,+∞)x=logayyx(0,+∞)R稱這兩個(gè)函數(shù)互為反函數(shù)對(duì)應(yīng)關(guān)系互逆指數(shù)函數(shù)y=ax是對(duì)數(shù)函數(shù)x=logay(a>0,a≠1)的反函數(shù)28優(yōu)秀課件指數(shù)函數(shù)y=ax與對(duì)數(shù)函數(shù)x=logay(a>0,a≠1)有指數(shù)函數(shù)y=ax(a>0,a≠1)對(duì)數(shù)函數(shù)y=logax(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29優(yōu)秀課件指數(shù)函數(shù)y=ax(a>0,a≠1)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=lgx;

(3)y=5x

【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，通過求出原來函數(shù)的值域來標(biāo)明反函數(shù)的定義域．30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)？31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1.32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＝loga(9－x)(a>0，a≠1)；(2)y＝log(x－1)(3－x)．33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＝1lg(x＋1)－3；

(2)y＝logx(2－x)．

34優(yōu)秀課件自我挑戰(zhàn)求下列函數(shù)的定義域：(1)y＝1lg(x＋1)－常見對(duì)數(shù)函數(shù)的圖像35優(yōu)秀課件常見對(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)y1＝log2x，y2＝log3x及y3＝log13x的圖像，并分析這些函數(shù)的性質(zhì)．

36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37優(yōu)秀課件【解】(1)列表17優(yōu)秀課件(2)描點(diǎn)(3)連線成圖．38優(yōu)秀課件(2)描點(diǎn)(3)連線成圖．18優(yōu)秀課件

(4)性質(zhì)：①定義域(0，＋∞)；②值域R；③y1＝log2x，y2＝log3x在(0，＋∞)上單調(diào)遞增．y3＝log13x在(0，＋∞)上單調(diào)遞減．④此三個(gè)函數(shù)過定點(diǎn)(1,