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1、雙雙向向固固基基礎(chǔ)礎(chǔ)點(diǎn)點(diǎn)面面講講考考向向多多元元提提能能力力教教師師備備用用題題返回目錄返回目錄返回目錄返回目錄 1 1指數(shù)函數(shù)指數(shù)函數(shù) (1) (1)了解指數(shù)函數(shù)模型的實(shí)際背景了解指數(shù)函數(shù)模型的實(shí)際背景 (2) (2)理解指數(shù)函數(shù)的概念，理解與指數(shù)函數(shù)性質(zhì)有關(guān)的理解指數(shù)函數(shù)的概念，理解與指數(shù)函數(shù)性質(zhì)有關(guān)的問(wèn)題問(wèn)題 2 2對(duì)數(shù)函數(shù)對(duì)數(shù)函數(shù)理解對(duì)數(shù)函數(shù)的概念；能解決與對(duì)數(shù)函數(shù)性質(zhì)有關(guān)的問(wèn)理解對(duì)數(shù)函數(shù)的概念；能解決與對(duì)數(shù)函數(shù)性質(zhì)有關(guān)的問(wèn)題題 3 3冪函數(shù)冪函數(shù) (1) (1)了解冪函數(shù)的概念了解冪函數(shù)的概念 (2) (2)結(jié)合函數(shù)結(jié)合函數(shù)y yx x，y yx x2 2，y yx x3 3，y y

2、 ，y y 的圖象，的圖象，了解它們的變化情況了解它們的變化情況考試說(shuō)明考試說(shuō)明第9講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄雙雙向向固固基基礎(chǔ)礎(chǔ)指數(shù)指數(shù)一、指數(shù)函數(shù)的概念、圖象與性質(zhì)一、指數(shù)函數(shù)的概念、圖象與性質(zhì)概念概念函數(shù)函數(shù)y ya ax x( (a a00，a a1)1)叫做叫做_函函數(shù)數(shù)底數(shù)底數(shù)a a1100a a100，a a1)1)叫做叫做_函數(shù)函數(shù)底底數(shù)數(shù)a a1100a a100時(shí)，冪函數(shù)的圖象通過(guò)原點(diǎn)，并且時(shí)，冪函數(shù)的圖象通過(guò)原點(diǎn)，并且在區(qū)間在區(qū)間_上是增函數(shù)上是增函數(shù)00時(shí)，冪函數(shù)的圖象在區(qū)間時(shí)，冪函數(shù)的圖象在區(qū)間(0(0，) )上是上是_函數(shù)在第一象限內(nèi)，當(dāng)函數(shù)在第一

3、象限內(nèi)，當(dāng)x x從從右邊趨向原點(diǎn)時(shí)，圖象在右邊趨向原點(diǎn)時(shí)，圖象在y y軸右方無(wú)限軸右方無(wú)限地逼近地逼近y y軸正半軸，當(dāng)軸正半軸，當(dāng)x x趨于趨于時(shí)，圖時(shí)，圖象在象在x x軸上方無(wú)限地逼近軸上方無(wú)限地逼近x x軸正半軸軸正半軸返回目錄返回目錄雙雙向向固固基基礎(chǔ)礎(chǔ)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄雙雙向向固固基基礎(chǔ)礎(chǔ)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄雙雙向向固固基基礎(chǔ)礎(chǔ)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄雙雙向向固固基基礎(chǔ)礎(chǔ)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)

4、、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄雙雙向向固固基基礎(chǔ)礎(chǔ)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄雙雙向向固固基基礎(chǔ)礎(chǔ)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考向向第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)考點(diǎn)考點(diǎn)考頻考頻示例示例( (難度難度) )1.1.指數(shù)函數(shù)的圖指數(shù)函數(shù)的圖象與性質(zhì)及應(yīng)用象與性質(zhì)及應(yīng)用選擇選擇(1)(1)20122012年浙江年浙江T9(B)T9(B)2.2.對(duì)數(shù)函數(shù)的圖對(duì)數(shù)函數(shù)的圖象與性質(zhì)及應(yīng)用象與性質(zhì)及應(yīng)用選擇選擇(1)(1)解答解答

5、(1)(1)20102010年浙江年浙江T10(C)T10(C)，20112011年浙江年浙江T22(C)T22(C)3.3.冪函數(shù)的圖象冪函數(shù)的圖象與性質(zhì)及應(yīng)用與性質(zhì)及應(yīng)用0 04.4.三種函數(shù)的綜三種函數(shù)的綜合應(yīng)用合應(yīng)用0 0說(shuō)明：說(shuō)明：A A表示簡(jiǎn)單題，表示簡(jiǎn)單題，B B表示中等題，表示中等題，C C表示難題，表示難題，考頻分析考頻分析2009200920122012年浙江卷情況年浙江卷情況 探究點(diǎn)一指數(shù)函數(shù)的圖象與性質(zhì)及應(yīng)用返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)

6、數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù) 點(diǎn)評(píng) (1)函數(shù)圖象判斷類試題的關(guān)鍵之一就是抓住函數(shù)圖象上的特殊點(diǎn)，如本題中令y0，解得x1，即無(wú)論a為何值，函數(shù)圖象過(guò)定點(diǎn)(1,0)，結(jié)合選項(xiàng)只有D中的圖象可能；(2)轉(zhuǎn)化是解決數(shù)學(xué)問(wèn)題的重要手段，本題中的定義實(shí)際上就是對(duì)任意的x(，1恒有f(x)K，進(jìn)一步轉(zhuǎn)化為函數(shù)f(x)在(，1上的最大值小于或者等于K，然后通過(guò)換元法再次把問(wèn)題轉(zhuǎn)化為我們熟悉的二次函數(shù)問(wèn)題返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函

7、數(shù)、冪函數(shù) 歸納總結(jié)函數(shù)圖象分析類試題要注意函數(shù)的性質(zhì)、函數(shù)圖象上特殊點(diǎn)的應(yīng)用從函數(shù)的性質(zhì)方面可以分析函數(shù)圖象的變化趨勢(shì)，從特殊點(diǎn)的位置可以確定可能的函數(shù)圖象或者否定一些函數(shù)圖象，在函數(shù)圖象分析中要注意正反方法的使用 指數(shù)函數(shù)最重要的性質(zhì)是它的單調(diào)性，在底數(shù)確定時(shí)直接使用指數(shù)函數(shù)的性質(zhì)，在底數(shù)不確定時(shí)要注意對(duì)底數(shù)進(jìn)行分類討論返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、

8、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù) 探究點(diǎn)二對(duì)數(shù)函數(shù)的圖象與性質(zhì)及應(yīng)用返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù) 點(diǎn)評(píng) (1)底數(shù)相同的指數(shù)函數(shù)、對(duì)數(shù)函數(shù)互為反函數(shù)，存在反函數(shù)的兩個(gè)函數(shù)互為反函數(shù)的充要條件是其圖象關(guān)于直線yx對(duì)稱；(2)在解對(duì)數(shù)不等式時(shí)一定不要忽視了對(duì)數(shù)的真數(shù)大于0，如果底數(shù)上含有自變量，則底數(shù)大于0且不等于1(見變式

9、(2)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù) 歸納總結(jié) 在解決與對(duì)數(shù)函數(shù)有關(guān)的問(wèn)題時(shí)一定要注意其定義域，一是真數(shù)大于0，二是底數(shù)大于0且不等于1，研究復(fù)合函數(shù)的單調(diào)性，一定要注意內(nèi)層與外層的單調(diào)性問(wèn)題復(fù)合函數(shù)的單調(diào)性的法則是“同增異減”返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、

10、冪函數(shù) 探究點(diǎn)三 冪函數(shù)的圖象與性質(zhì)及應(yīng)用返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講

11、講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù) 探究點(diǎn)四 三種函數(shù)的綜合應(yīng)用返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù) 返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù) 點(diǎn)評(píng)使用函數(shù)性質(zhì)比較一些數(shù)值的大小要解決兩個(gè)問(wèn)題(1)構(gòu)造指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)，如果是指數(shù)式時(shí)，若底數(shù)相同則構(gòu)造指數(shù)函數(shù)、若指數(shù)相同則構(gòu)造冪函數(shù)；(2)善于把所求 的 數(shù)值通過(guò)逐步縮小范圍的方法把其限

12、定在某個(gè)區(qū)間之內(nèi)，通過(guò)不同區(qū)間內(nèi)數(shù)值大小關(guān)系判斷所要解決的數(shù)值大小問(wèn)題返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄點(diǎn)點(diǎn)面面講講考考點(diǎn)點(diǎn)第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)易錯(cuò)究源易錯(cuò)究源5 5函數(shù)的性質(zhì)使用不當(dāng)致誤函數(shù)的性質(zhì)使用不當(dāng)致誤返回目錄返回目錄多多元元提提能能力力第第9 9講講指數(shù)函

13、數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄多多元元提提能能力力第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄多多元元提提能能力力第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄多多元元提提能能力力第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)【備選理由備選理由】 高考中指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)往往是與函數(shù)的高考中指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)往往是與函數(shù)的奇偶性、不等式的解、函數(shù)與方程、不等式等問(wèn)題綜合進(jìn)奇偶性、不等式的解、函數(shù)與方程、不等式等問(wèn)題綜合進(jìn)行考查的，在正文中為突出各個(gè)探究點(diǎn)

14、的主體，我們沒(méi)有行考查的，在正文中為突出各個(gè)探究點(diǎn)的主體，我們沒(méi)有過(guò)多綜合，下面的例過(guò)多綜合，下面的例1 1是函數(shù)奇偶性與對(duì)數(shù)函數(shù)的綜合，是函數(shù)奇偶性與對(duì)數(shù)函數(shù)的綜合，例例2 2從函數(shù)方程的觀點(diǎn)考查指數(shù)函數(shù)與對(duì)數(shù)函數(shù)，例從函數(shù)方程的觀點(diǎn)考查指數(shù)函數(shù)與對(duì)數(shù)函數(shù)，例3 3從函從函數(shù)圖象入手，看似對(duì)數(shù)函數(shù)問(wèn)題最后要化為指數(shù)函數(shù)進(jìn)行數(shù)圖象入手，看似對(duì)數(shù)函數(shù)問(wèn)題最后要化為指數(shù)函數(shù)進(jìn)行解決，這三個(gè)題目都具有一定的綜合性，可以作為本講相解決，這三個(gè)題目都具有一定的綜合性，可以作為本講相應(yīng)探究點(diǎn)的補(bǔ)充，也可作為本講總結(jié)之用應(yīng)探究點(diǎn)的補(bǔ)充，也可作為本講總結(jié)之用返回目錄返回目錄教教師師備備用用題題第第9 9講講指

15、數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄教教師師備備用用題題第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄教教師師備備用用題題第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄教教師師備備用用題題第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄教教師師備備用用題題第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄教教師師備備用用題題第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄教教師師備備用用題題第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)返回目錄返回目錄教教師師備備用用題題第第9 9講講指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)