《對數(shù)函數(shù)及其性質(zhì)》第三課時參考課件

1、 2.2對數(shù)函數(shù)2.2.2對數(shù)函數(shù)及其性質(zhì)第三課時習(xí)題課形形 式式圖圖 象象定義域定義域 值值 域域特特 征征函數(shù)值函數(shù)值的變化的變化單調(diào)性單調(diào)性關(guān)關(guān) 系系yxo)1 ,0(1 y)1( aayx) 10 ( aayx)10(log axya1 xyxo)0,1()1(log axya)1, 0(log aaxya),(), 0( )1, 0( aaayx),(), 0( )0 , 1(過過定定點點)1 , 0(過過定定點點 ).0( 1),0( 1),0( 1xxxax ).0( 1),0( 1),0( 1xxxax1 a10 a ).10(0),1(0),1(0logxxxxa ).10(

2、0),1(0),1(0logxxxxa1 a10 a增函數(shù)增函數(shù)減函數(shù)減函數(shù).,log對對稱稱圖圖象象關(guān)關(guān)于于直直線線互互為為反反函函數(shù)數(shù)與與xyxyayax 增函數(shù)增函數(shù)減函數(shù)減函數(shù)復(fù)習(xí)與回顧復(fù)習(xí)與回顧: :指數(shù)函數(shù)與對數(shù)函數(shù)性質(zhì)和圖象指數(shù)函數(shù)與對數(shù)函數(shù)性質(zhì)和圖象1. 1.求定義域和值域求定義域和值域. .)32(log1lg)2()1(1)2(log1)1(.)5(1ln21 xxyxxyx義義域域例例求求下下列列函函數(shù)數(shù)的的定定.)23(log:22 . 0的值域的值域求函數(shù)求函數(shù)【例】【例】xxy ）5 , 4()4 , 2()2 ,23)(2();2 , 1 () 1 , 0)(1

3、( 2log,(2 . 0 .,)2lg(22的的取取值值范范圍圍求求實實數(shù)數(shù)的的定定義義域域為為若若函函數(shù)數(shù)變變題題aRaxxy 2.2.求取值范圍求取值范圍. .)., 0.(),21.21, 0.()21, 0.()(, 0)()1(log)()0 , 1(2 DCBAaxfxxfa的的取取值值范范圍圍則則滿滿足足內(nèi)內(nèi)的的函函數(shù)數(shù)【例例】若若定定義義在在區(qū)區(qū)間間.,)2lg(22的的取取值值范范圍圍求求實實數(shù)數(shù)的的值值域域為為若若函函數(shù)數(shù)例例aRaxxy 1 , 1 ), 1()1,( 1., 1., 10 ., 10 .)(, 02log2log abDbaCabBbaAba則則例例若

4、若3.3.比較大小比較大小. .8 . 0log, 8 . 0log)4(;7log, 7log)3(.ln,14. 3ln)2(; 9 . 5log, 1 . 5log)1(:3 . 02 . 032 aa例例比比較較大大小小4.4.綜合應(yīng)用綜合應(yīng)用.)2)(log4(log)(, 03)(log7)(log2:2221221的最值的最值求函數(shù)求函數(shù)滿足不等式滿足不等式已知已知例例xxxfxxx 3log21, 03)(log7)(log2:221221 xxx解解)321(23)(,log2log3)(log)2)(log4(log)(2222222 tttxfxtxxxxxf有有令令2)

5、(, 8, 3log,341)(,22,23log,23max2min2 xfxxtxfxxt即即時時當(dāng)當(dāng)即即時時當(dāng)當(dāng).)3(;0)(,1)2(;)1()1, 0(11log)(討論函數(shù)的單調(diào)性討論函數(shù)的單調(diào)性取值范圍取值范圍的的求使求使時時當(dāng)當(dāng)求定義域求定義域例設(shè)函數(shù)例設(shè)函數(shù)xxfaaaxxxfa 4.4.綜合應(yīng)用綜合應(yīng)用.)412lg(2單單調(diào)調(diào)增增區(qū)區(qū)間間【例例】求求xxy ._,)1 , 01(log取取范范圍圍的的求求上上是是增增函函數(shù)數(shù)在在）【例例】若若函函數(shù)數(shù)axya ), 2.)2 , 0.()2 , 1.()1 , 0.()(,1 , 02(log DCBAaaxya范范圍圍

6、是是的的取取求求上上是是減減函函數(shù)數(shù)在在）【例例】若若函函數(shù)數(shù)2, 6( )1 , 0(5.5.單調(diào)性（備選）單調(diào)性（備選）1)1(log.1)1(log.1)1(log.1)1(log.)(,2:222233221 xyDxyCxyBxyACCxyCCCyx的的解解析析式式為為則則的的對對稱稱圖圖形形得得到到關(guān)關(guān)于于直直線線再再作作向向上上平平移移一一個個單單位位得得位位得得的的圖圖象象向向左左平平移移一一個個單單將將例例), 2()21, 0.()2 , 1.()2 , 1()21, 0.()2 , 1()1 ,21.()(, 1|), 2log: DCBAayxya的取值范圍是的取值范圍是則實數(shù)則實數(shù)上恒有上恒有在在函數(shù)函數(shù)例例5.5.（備選）（備選）._,0log02. 42 則則的根分別是的根分別是與方程與方程已知