《[優(yōu)化設(shè)計(jì)]新人教A版數(shù)學(xué)高中必修一2.2《對(duì)數(shù)函數(shù)》(公開課)》由會(huì)員分享,可在線閱讀,更多相關(guān)《[優(yōu)化設(shè)計(jì)]新人教A版數(shù)學(xué)高中必修一2.2《對(duì)數(shù)函數(shù)》(公開課)(25頁(yè)珍藏版)》請(qǐng)?jiān)谘b配圖網(wǎng)上搜索。
1、對(duì)數(shù)函數(shù)的圖像和性質(zhì)對(duì)數(shù)函數(shù)的圖像和性質(zhì) 咸陽(yáng)師院附屬中學(xué)咸陽(yáng)師院附屬中學(xué) 殷敏殷敏一一.復(fù)習(xí)對(duì)數(shù)函數(shù)的概念復(fù)習(xí)對(duì)數(shù)函數(shù)的概念 圖 象 性 質(zhì)yx0y=1(0,1)y=ax(a1)yx(0,1)y=10y=ax(0a10a 0 時(shí),y 1.當(dāng) x 0 時(shí),. 0 y 1當(dāng) x 1;當(dāng) x 0 時(shí), 0 y 10a1時(shí)時(shí),y00 x1時(shí)時(shí),y00 x0 x1時(shí)時(shí),y得得 0 x 函數(shù)函數(shù) 2logayx=的定義域是的定義域是|0 x x log (4)ayx=-由由 40 x-得得 4x 函數(shù)函數(shù) 的定義域是的定義域是log (4)ayx=-|4x x 得得 函數(shù)函數(shù) 的定義域是的定義域是2lo
2、g (9)ayx=-(0,1)(1, 3)應(yīng)用:應(yīng)用:和和 例2 比較下列各組數(shù)中兩個(gè)值的大?。?log 23.4 , log 28.5 log 0.31.8 , log 0.32.7 log a5.1 , log a5.9 ( a0 , a1 ) 解解:考察對(duì)數(shù)函數(shù)考察對(duì)數(shù)函數(shù) y = log 2x,所以它在所以它在(0,+)上是增函數(shù)上是增函數(shù),于是于是log 23.4log 28.5考察對(duì)數(shù)函數(shù)考察對(duì)數(shù)函數(shù) y = log 0.3 x,因?yàn)樗牡讛?shù)為因?yàn)樗牡讛?shù)為0.3,即即00.31,所以它在所以它在(0,+)上是減函數(shù)上是減函數(shù),于是于是log 0.31.8log 0.32.7因?yàn)樗?/p>
3、的底數(shù)因?yàn)樗牡讛?shù)21, log a5.1 , log a5.9 ( a0 , a1 )(對(duì)數(shù)函數(shù)的增減性決定于對(duì)數(shù)的底數(shù)是大于對(duì)數(shù)函數(shù)的增減性決定于對(duì)數(shù)的底數(shù)是大于1還是小于還是小于1. 而已知條件中并未指出底數(shù)而已知條件中并未指出底數(shù)a與與1哪個(gè)大哪個(gè)大,因此需要對(duì)底數(shù)因此需要對(duì)底數(shù)a進(jìn)行討論進(jìn)行討論)解解:當(dāng)當(dāng)a1時(shí)時(shí),函數(shù)函數(shù)y=log ax在在(0,+)上是增函數(shù)上是增函數(shù),于是于是 當(dāng)當(dāng)0a1時(shí)時(shí),函數(shù)函數(shù)y=log ax在在(0,+)上是減函數(shù)上是減函數(shù),于是于是log a5.1log a5.9log a5.1log a5.9例例3 比較下列各組中兩個(gè)值的大小比較下列各組中兩個(gè)值
4、的大小: log 67 , log 7 6 ; log 3 , log 2 0.8 . 解解: log67log661 log20.8log210 : log a1=0 log76log771 log67log76 log3log310 log3log20.8圖象性 質(zhì) 對(duì)數(shù)函數(shù)y=log a x (a0, a1)指數(shù)函數(shù)y=ax (a0,a1)(4) a1時(shí)時(shí), x0,0y0,y1 0a1時(shí)時(shí),x1;x0,0y1時(shí)時(shí),0 x1,y1,y0 0a1時(shí)時(shí),0 x0; x1,y1時(shí)時(shí), 在在R上是增函數(shù);上是增函數(shù); 0a1時(shí)時(shí),在在(0,+)是增函數(shù);是增函數(shù); 0a1) y=ax (0a1)y=logax (0a1)xyo1(2)看見函數(shù)式想圖像,結(jié)合圖像記)看見函數(shù)式想圖像,結(jié)合圖像記性質(zhì)。性質(zhì)。(1) 類比記憶指數(shù)函數(shù)和對(duì)數(shù)函數(shù)。類比記憶指數(shù)函數(shù)和對(duì)數(shù)函數(shù)。比較大?。罕容^大?。海?) (2)35lo glo g22 和351loglog21和2提示:此種比較大小屬于提示:此種比較大小屬于“同真同真”.習(xí)題習(xí)題3-5 3,4