高中數(shù)學(xué)《對(duì)數(shù)函數(shù)》教案17新人教A版必修1

對(duì)數(shù)函數(shù)教課目的:(1)經(jīng)過詳細(xì)實(shí)例,直觀認(rèn)識(shí)對(duì)數(shù)函數(shù)模型所刻畫的數(shù)目關(guān)系，初步理解對(duì)數(shù)函數(shù)的觀點(diǎn),領(lǐng)會(huì)對(duì)數(shù)函數(shù)是一類重要的函數(shù)模型；經(jīng)過對(duì)數(shù)函數(shù)的圖象探究并認(rèn)識(shí)對(duì)數(shù)函數(shù)的單一性與特別點(diǎn)；經(jīng)過比較、比較的方法,指引學(xué)生聯(lián)合圖象類比指數(shù)函數(shù),探究研究對(duì)數(shù)函數(shù)的性質(zhì),培育學(xué)生數(shù)形聯(lián)合的思想方法,學(xué)會(huì)研究函數(shù)性質(zhì)的方法．教課要點(diǎn):掌握對(duì)數(shù)函數(shù)的圖象和性質(zhì)．教課難點(diǎn):對(duì)數(shù)函數(shù)的定義，對(duì)數(shù)函數(shù)的圖象和性質(zhì)及應(yīng)用．教課過程:.知識(shí)鏈接學(xué)習(xí)指數(shù)函數(shù)時(shí)，對(duì)其性質(zhì)研究了哪些內(nèi)容？對(duì)數(shù)的定義及其對(duì)底數(shù)的限制．二.問題情境填寫下表：(課本45頁開篇的細(xì)胞分裂問題中得出的指數(shù)函數(shù)y2x)y2481632x【思慮:有何發(fā)現(xiàn)?】三.建構(gòu)數(shù)學(xué)1.對(duì)數(shù)函數(shù)的觀點(diǎn):一般地,函數(shù)ylogax(a0，且a1)叫做對(duì)數(shù)函數(shù)（logarithmicfunction）,此中x是自變量,函數(shù)的定義域是（0,+∞）．注意:(1)對(duì)數(shù)函數(shù)的定義與指數(shù)函數(shù)近似,都是形式定義,注意鑒別.如：y2log2x，ylog5x都不是對(duì)數(shù)函數(shù)，而只好稱其為對(duì)數(shù)型函數(shù)．5(2)對(duì)數(shù)函數(shù)對(duì)底數(shù)的限制：(a0，且a1)．2.對(duì)數(shù)函數(shù)的圖象和性質(zhì)【問題】類比前面議論指數(shù)函數(shù)性質(zhì)的思路,提出研究對(duì)數(shù)函數(shù)性質(zhì)的內(nèi)容!1.在同一坐標(biāo)系中畫出以下對(duì)數(shù)函數(shù)的圖象:(1)ylog2x(2)ylog1x(3)ylog3x(4)ylog1x232.聯(lián)合圖像研究對(duì)數(shù)函數(shù)ylogax的性質(zhì)：對(duì)數(shù)函數(shù)ylogax(a0,且a1)底數(shù)范圍a>10<a<1定義域值域單一性奇偶性圖像特色函數(shù)的圖像恒過定點(diǎn)對(duì)稱性(1)和(2)的圖像對(duì)于對(duì)稱結(jié)論x>1時(shí),底數(shù)越大越x>1時(shí),底數(shù)越大越四.數(shù)學(xué)應(yīng)用例1.求以下函數(shù)的定義域:例2.利用對(duì)數(shù)函數(shù)的性質(zhì),比較以下各組數(shù)中兩個(gè)數(shù)的大小:(1)log23.4,log23.8(2)log0.51.8,log0.52.1(3)log75,log67【練習(xí)：課本62頁.練習(xí)2、3】例3.說明函數(shù)ylog3(x2)與函數(shù)ylog3x的圖像的關(guān)系,并在一個(gè)平面坐標(biāo)系內(nèi)畫出它們的圖像.【思慮】(1)函數(shù)yloga(xb)與函數(shù)ylogax(a0,a1,b0)的圖像之間有什么關(guān)系?(2)函數(shù)yfx與函數(shù)yfxm的圖像之間有什么關(guān)系?(3)函數(shù)yfx與函數(shù)yfxn的圖像之間有什么關(guān)系?例3.在同一平面坐標(biāo)系內(nèi)畫出函數(shù)y2x與函數(shù)ylog2x的圖像,并說明它們有何關(guān)系?【反函數(shù)】一般說來,設(shè)A,B分別為函數(shù)yf(x)的定義域和值域,假如由函數(shù)yf(x)所解得的x(y)也是一個(gè)函數(shù)(即對(duì)隨意一個(gè)yB,都有唯一的xA與之對(duì)應(yīng)),那么就稱函數(shù)x(y)是函數(shù)yf(x)的反函數(shù)(inversefunction),記做xf1(y).在xf1(y)中,y是自變量,x是y的函數(shù).習(xí)慣上常改寫成yf1(x)xB,yA的形式.【練習(xí)】以下函數(shù)能否存在反函數(shù),若存在,求出其反函數(shù):2.(1)函數(shù)y3x與函數(shù)ylog3x的圖像對(duì)于對(duì)稱;(2)函數(shù)yf(x)的圖像經(jīng)過點(diǎn)(1,3),則其反函數(shù)的圖像必經(jīng)過點(diǎn).五.回首小結(jié)掌握對(duì)數(shù)函數(shù)的觀點(diǎn),嫻熟運(yùn)用對(duì)數(shù)函數(shù)圖象和性質(zhì);理解反函數(shù)觀點(diǎn),理解不是全部的函數(shù)都存在反函數(shù);反函數(shù)的性質(zhì):(1)互為反函數(shù)的兩個(gè)函數(shù)的圖像對(duì)于直線yx對(duì)稱;(2)互為反函數(shù)的兩個(gè)函數(shù)之間定義域與值域的關(guān)系;若函數(shù)y