數(shù)學(xué)23對(duì)數(shù)函數(shù)概念以及圖象性質(zhì)(蘇教版必修課件

1、2xy xy、2logxyx2logyxy 一般地,函數(shù) y = loga x (a0,且a 1 )叫做對(duì)數(shù)函數(shù).其中 x是自變量,函數(shù)的定義域是（函數(shù)的定義域是（ 0 , +0 , +）. .對(duì)數(shù)函數(shù)的定義：對(duì)數(shù)函數(shù)的定義：注意注意:1):1)對(duì)數(shù)函數(shù)定義的嚴(yán)格形式對(duì)數(shù)函數(shù)定義的嚴(yán)格形式; ;0a. 1a，且，且2)對(duì)數(shù)函數(shù)對(duì)底數(shù)的限制條件：對(duì)數(shù)函數(shù)對(duì)底數(shù)的限制條件： 221lo g2lo g(4)3lo g(9)aaayxyxyx分析：應(yīng)用定義中的條件解決.答案： 10 ; 2, 433,3x x log0,1ayx aa且212lo glo gyxyx和 yf xyf x 與的圖象有什么

2、關(guān)系？列表列表描點(diǎn)描點(diǎn)連線連線21-1-21240yx32114xy2log -2 -1 0 1 2xy21log這兩個(gè)函這兩個(gè)函數(shù)的圖象數(shù)的圖象有什么關(guān)有什么關(guān)系呢？系呢？關(guān)于關(guān)于x軸對(duì)稱軸對(duì)稱 對(duì)數(shù)函數(shù)對(duì)數(shù)函數(shù) 的圖象。的圖象。xyxy313loglog 和和猜猜猜猜: 21-1-21240yx32114xy2log xy21log xy3log xy31log 底數(shù)底數(shù)a1時(shí)時(shí),底數(shù)越底數(shù)越大大,其其圖象越接近圖象越接近x軸。軸。底數(shù)底數(shù)0a1a10a10a1a1時(shí)，時(shí)， x(0,1)x(0,1)時(shí)，時(shí)，y0y0 ,y0 當(dāng)當(dāng)0a10a1a1時(shí)，時(shí)，y=logy=loga ax x在在(

3、 0,( 0,) ) 是是增增函數(shù)函數(shù); ;當(dāng)當(dāng)0a10a log0.5(1-x)(2) log2(x+3) 2 (1)1,loglog0aaamnmn若(2)01,loglog0aaamnmn若依據(jù)依據(jù)：(3)log21x指數(shù)函數(shù)圖像與對(duì)指數(shù)函數(shù)圖像與對(duì)幾何畫板幾何畫板.lnk數(shù)函數(shù)的圖像的關(guān)系數(shù)函數(shù)的圖像的關(guān)系2xy 2logyx8642-2-4-6-8-10-5510y=f(x)h x g x f x x y =log xa y =log xa00(1,0)(1,0) x=1 x=1( a1)(0 a1)y y xx再見！再見！12logyx2logyx13logyx3logyx10 xy1x 0.30.31 loglog.2 loglog.aamnmn,m n分析：從對(duì)數(shù)函數(shù)的單調(diào)性入手分析：從對(duì)數(shù)函數(shù)的單調(diào)性入手. 2220.11log23 ;2log253 .yxxyxx分析：關(guān)鍵是把握好復(fù)合函數(shù)單調(diào)性的判斷.aa分析：一是要把握住對(duì)數(shù)函數(shù)的單調(diào)性； 二是要注意分類討論.1,1.01 ,.0,1,.aaaa