基本初等函數(shù)總復(fù)習(xí)

精品文檔精品文檔精品文檔精品文檔精品文檔精品文檔指數(shù)函數(shù)總復(fù)習(xí)【知識(shí)點(diǎn)回顧】一、指數(shù)與指數(shù)冪的運(yùn)算（1）根式的概念①如果SKIPIF1<0，且SKIPIF1<0，那么SKIPIF1<0叫做SKIPIF1<0的SKIPIF1<0次方根．當(dāng)SKIPIF1<0是奇數(shù)時(shí)，SKIPIF1<0的SKIPIF1<0次方根用符號(hào)SKIPIF1<0表示；當(dāng)SKIPIF1<0是偶數(shù)時(shí)，正數(shù)SKIPIF1<0的正的SKIPIF1<0次方根用符號(hào)SKIPIF1<0表示，負(fù)的SKIPIF1<0次方根用符號(hào)SKIPIF1<0表示；0的SKIPIF1<0次方根是0；負(fù)數(shù)SKIPIF1<0沒有SKIPIF1<0次方根．②式子SKIPIF1<0叫做根式，這里SKIPIF1<0叫做根指數(shù)，SKIPIF1<0叫做被開方數(shù)．當(dāng)SKIPIF1<0為奇數(shù)時(shí)，SKIPIF1<0為任意實(shí)數(shù)；當(dāng)SKIPIF1<0為偶數(shù)時(shí)，SKIPIF1<0．③根式的性質(zhì)：SKIPIF1<0；當(dāng)SKIPIF1<0為奇數(shù)時(shí)，SKIPIF1<0；當(dāng)SKIPIF1<0為偶數(shù)時(shí)，SKIPIF1<0．（2）分?jǐn)?shù)指數(shù)冪的概念①正數(shù)的正分?jǐn)?shù)指數(shù)冪的意義是：SKIPIF1<0且SKIPIF1<0．0的正分?jǐn)?shù)指數(shù)冪等于0．②正數(shù)的負(fù)分?jǐn)?shù)指數(shù)冪的意義是：SKIPIF1<0且SKIPIF1<0．0的負(fù)分?jǐn)?shù)指數(shù)冪沒有意義．注意口訣：底數(shù)取倒數(shù)，指數(shù)取相反數(shù)．（3）分?jǐn)?shù)指數(shù)冪的運(yùn)算性質(zhì)①SKIPIF1<0②SKIPIF1<0③SKIPIF1<0二、指數(shù)函數(shù)及其性質(zhì)（4）指數(shù)函數(shù)函數(shù)名稱指數(shù)函數(shù)定義函數(shù)SKIPIF1<0且SKIPIF1<0叫做指數(shù)函數(shù)圖象SKIPIF1<0SKIPIF1<0001001定義域SKIPIF1<0值域（0,+∞）過定點(diǎn)圖象過定點(diǎn)（0,1），即當(dāng)x=0時(shí)，y=1．奇偶性非奇非偶單調(diào)性在SKIPIF1<0上是增函數(shù)在SKIPIF1<0上是減函數(shù)函數(shù)值的變化情況y＞1(x＞0),y=1(x=0),0＜y＜1(x＜0)y＞1(x＜0),y=1(x=0),0＜y＜1(x＞0)SKIPIF1<0變化對(duì)圖象的影響在第一象限內(nèi)，SKIPIF1<0越大圖象越高，越靠近y軸；在第二象限內(nèi)，SKIPIF1<0越大圖象越低，越靠近x軸．在第一象限內(nèi)，SKIPIF1<0越小圖象越高，越靠近y軸；在第二象限內(nèi)，SKIPIF1<0越小圖象越低，越靠近x軸．【考點(diǎn)鏈接】考點(diǎn)一、指數(shù)的運(yùn)算例1．化簡：．例2.根據(jù)下列條件求值：已知SKIPIF1<0，求SKIPIF1<0的值；練習(xí)1：計(jì)算：（1）（2）．(3)SKIPIF1<0（4）SKIPIF1<0考點(diǎn)二、定義域例3．求下列函數(shù)的定義域：練習(xí)2．求下列函數(shù)的定義域:（1）（2）考點(diǎn)三、值域例4．函數(shù)的值域練習(xí)3、(1)求函數(shù)的值域．(2)求下列函數(shù)的定義域、值域：（1）SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1<0考點(diǎn)四、指數(shù)型函數(shù)例5.已知函數(shù)SKIPIF1<0的定義域?yàn)閇0，1]，則值域?yàn)?。練?xí)4.若方程SKIPIF1<0有正數(shù)解，則實(shí)數(shù)SKIPIF1<0的取值范圍是考點(diǎn)五、函數(shù)的奇偶性與解析式例6．（1）函數(shù)是奇函數(shù),且當(dāng)時(shí),,則時(shí),_____．（2）設(shè)是上的偶函數(shù),則________________．練習(xí)5．（1）定義在上的函數(shù)是奇函數(shù),且當(dāng)時(shí),,則時(shí),__________．（2）已知函數(shù),若為奇函數(shù),則________________．（3）已知SKIPIF1<0，試判定SKIPIF1<0的奇偶性?？键c(diǎn)五、函數(shù)的單調(diào)性例7．（1）比較下列各組數(shù)的大小：（1）和；

（2）和；（3）和

．

（2）試比較SKIPIF1<0，SKIPIF1<0三者之間的大小關(guān)系。例8.已知函數(shù)SKIPIF1<0，（1）求使SKIPIF1<0成立的x值；（2）求使SKIPIF1<0、SKIPIF1<0均為增函數(shù)的單調(diào)區(qū)間；（3）求SKIPIF1<0和SKIPIF1<0的值域。練習(xí)6．（1）比較下列各組數(shù)的大?。海?）和；

（2）和；（3）和

．（2）設(shè)SKIPIF1<0，SKIPIF1<0，試確定SKIPIF1<0的大小關(guān)系?？键c(diǎn)六、綜合應(yīng)用例9．已知函數(shù)．（1）求的定義域和值域；（2）討論單調(diào)性．例10.已知函數(shù)SKIPIF1<0，其中SKIPIF1<0，是R上的增函數(shù)，求a的取值范圍。練習(xí)7.已知函數(shù)．（1）求的定義域和值域；（2）討論單調(diào)性．練習(xí)8.設(shè)SKIPIF1<0。（1）寫出函數(shù)SKIPIF1<0與SKIPIF1<0的定義域。（2）函數(shù)SKIPIF1<0與SKIPIF1<0是否具有奇偶性，并說明理由。（3）求出函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間?！菊n后練習(xí)】一、選擇題：1．某種細(xì)菌在培養(yǎng)過程中，每SKIPIF1<0分鐘分裂一次（一個(gè)分裂為兩個(gè)）。經(jīng)過SKIPIF1<0個(gè)小時(shí)，這種細(xì)菌由SKIPIF1<0個(gè)可繁殖成（）SKIPIF1<0個(gè)SKIPIF1<0個(gè)SKIPIF1<0個(gè)SKIPIF1<0個(gè)2．在統(tǒng)一平面直角坐標(biāo)系中，函數(shù)SKIPIF1<0與SKIPIF1<0的圖像可能是（）3．設(shè)SKIPIF1<0都是不等于SKIPIF1<0的正數(shù)，SKIPIF1<0在同一坐標(biāo)系中的圖像如圖所示，則SKIPIF1<0的大小順序是（）SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0 4.函數(shù)SKIPIF1<0滿足SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0與SKIPIF1<0的大小關(guān)系是（）A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.不能確定5.若SKIPIF1<0，那么下列各不等式成立的是（）SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<06.函數(shù)SKIPIF1<0在SKIPIF1<0上是減函數(shù)，則SKIPIF1<0的取值范圍是（）SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<07．函數(shù)SKIPIF1<0的值域是（）SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<08．當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0是（）SKIPIF1<0奇函數(shù)SKIPIF1<0偶函數(shù)SKIPIF1<0既奇又偶函數(shù)SKIPIF1<0非奇非偶函數(shù)9．函數(shù)SKIPIF1<0且SKIPIF1<0的圖像必經(jīng)過點(diǎn)（）SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<010．某廠1998年的產(chǎn)值為SKIPIF1<0萬元，預(yù)計(jì)產(chǎn)值每年以SKIPIF1<0％遞增，則該廠到2010年的產(chǎn)值（單位：萬元）是（）SKIPIF1<0％SKIPIF1<0SKIPIF1<0％SKIPIF1<0SKIPIF1<0％SKIPIF1<0SKIPIF1<0％SKIPIF1<0二、填空題：已知SKIPIF1<0是指數(shù)函數(shù)，且SKIPIF1<0，則SKIPIF1<0設(shè)SKIPIF1<0，使不等式SKIPIF1<0成立的SKIPIF1<0的集合是函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為SKIPIF1<0三、解答題：1．設(shè)SKIPIF1<0，求函數(shù)SKIPIF1<0的最大值和最小值。2函數(shù)SKIPIF1<0且SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值比最小值大SKIPIF1<0，求SKIPIF1<0的值。3．設(shè)SKIPIF1<0，SKIPIF1<0試確定SKIPIF1<0的值，使SKIPIF1<0為奇函數(shù)。4．已知函數(shù)SKIPIF1<0（1）求函數(shù)的定義域及值域；（2）確定函數(shù)的單調(diào)區(qū)間。5．已知函數(shù)SKIPIF1<0（1）求函數(shù)的定義域；（2）討論函數(shù)的奇偶性；（3）證明：SKIPIF1<0對(duì)數(shù)函數(shù)總復(fù)習(xí)【知識(shí)點(diǎn)回顧】一、對(duì)數(shù)與對(duì)數(shù)運(yùn)算對(duì)數(shù)的定義①若SKIPIF1<0，則SKIPIF1<0叫做以SKIPIF1<0為底SKIPIF1<0的對(duì)數(shù)，記作SKIPIF1<0，其中SKIPIF1<0叫做底數(shù)，SKIPIF1<0叫做真數(shù)．②負(fù)數(shù)和零沒有對(duì)數(shù)．③對(duì)數(shù)式與指數(shù)式的互化：SKIPIF1<0．（2）幾個(gè)重要的對(duì)數(shù)恒等式:SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．（3）常用對(duì)數(shù)與自然對(duì)數(shù)：常用對(duì)數(shù)：SKIPIF1<0，即SKIPIF1<0；自然對(duì)數(shù)：SKIPIF1<0，即SKIPIF1<0（其中SKIPIF1<0…）．（4）對(duì)數(shù)的運(yùn)算性質(zhì)如果SKIPIF1<0，那么①加法：SKIPIF1<0②減法：SKIPIF1<0③數(shù)乘：SKIPIF1<0④SKIPIF1<0⑤SKIPIF1<0⑥換底公式：SKIPIF1<0二、對(duì)數(shù)函數(shù)及其性質(zhì)（5）對(duì)數(shù)函數(shù)函數(shù)名稱對(duì)數(shù)函數(shù)定義函數(shù)SKIPIF1<0且SKIPIF1<0叫做對(duì)數(shù)函數(shù)圖象SKIPIF1<0SKIPIF1<0001001定義域SKIPIF1<0值域SKIPIF1<0過定點(diǎn)圖象過定點(diǎn)SKIPIF1<0，即當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．奇偶性非奇非偶單調(diào)性在SKIPIF1<0上是增函數(shù)在SKIPIF1<0上是減函數(shù)函數(shù)值的變化情況SKIPIF1<0SKIPIF1<0SKIPIF1<0變化對(duì) 圖象的影響在第一象限內(nèi)，SKIPIF1<0越大圖象越靠低，越靠近x軸在第四象限內(nèi)，SKIPIF1<0越大圖象越靠高，越靠近y軸在第一象限內(nèi)，SKIPIF1<0越小圖象越靠低，越靠近x軸在第四象限內(nèi)，SKIPIF1<0越小圖象越靠高，越靠近y軸(6)反函數(shù)的概念設(shè)函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，值域?yàn)镾KIPIF1<0，從式子SKIPIF1<0中解出SKIPIF1<0，得式子SKIPIF1<0．如果對(duì)于SKIPIF1<0在SKIPIF1<0中的任何一個(gè)值，通過式子SKIPIF1<0，SKIPIF1<0在SKIPIF1<0中都有唯一確定的值和它對(duì)應(yīng)，那么式子SKIPIF1<0表示SKIPIF1<0是SKIPIF1<0的函數(shù)，函數(shù)SKIPIF1<0叫做函數(shù)SKIPIF1<0的反函數(shù)，記作SKIPIF1<0，習(xí)慣上改寫成SKIPIF1<0．（7）反函數(shù)的求法①確定反函數(shù)的定義域，即原函數(shù)的值域；②從原函數(shù)式SKIPIF1<0中反解出SKIPIF1<0；③將SKIPIF1<0改寫成SKIPIF1<0，并注明反函數(shù)的定義域．（8）反函數(shù)的性質(zhì)①原函數(shù)SKIPIF1<0與反函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱．②函數(shù)SKIPIF1<0的定義域、值域分別是其反函數(shù)SKIPIF1<0的值域、定義域．③若SKIPIF1<0在原函數(shù)SKIPIF1<0的圖象上，則SKIPIF1<0在反函數(shù)SKIPIF1<0的圖象上．④一般地，函數(shù)SKIPIF1<0要有反函數(shù)則它必須為單調(diào)函數(shù)．【考點(diǎn)鏈接】考點(diǎn)一、對(duì)數(shù)的運(yùn)算例1、（1）計(jì)算：SKIPIF1<0，SKIPIF1<0．（2）求x的值：①SKIPIF1<0；②SKIPIF1<0．（3）求底數(shù)：①已知SKIPIF1<0，求SKIPIF1<0的值 ②SKIPIF1<0，求SKIPIF1<0的值 （4）已知SKIPIF1<0，求SKIPIF1<0的值例2、計(jì)算：（1）lg14SKIPIF1<021gSKIPIF1<0；（2）SKIPIF1<0；（3）SKIPIF1<0．練習(xí)1、計(jì)算：（1）SKIPIF1<0；（2）SKIPIF1<0．練習(xí)2、已知SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0（用a,b表示）．練習(xí)3、設(shè)SKIPIF1<0，求證：SKIPIF1<0．練習(xí)4、若SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0．考點(diǎn)二、函數(shù)的定義域例3、求下列函數(shù)的定義域：SKIPIF1<0；（2）SKIPIF1<0；（3）SKIPIF1<0．練習(xí)5、求下列函數(shù)的定義域：（1）SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1<0（4）SKIPIF1<0（5）SKIPIF1<0考點(diǎn)三、函數(shù)的值域例4、求下列函數(shù)的值域：（1）SKIPIF1<0；（2）SKIPIF1<0；（3）SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）．練習(xí)6、求下列函數(shù)的值域(1)SKIPIF1<0(2)SKIPIF1<0考點(diǎn)五、對(duì)數(shù)函數(shù)的單調(diào)性例5、比較下列各組數(shù)中兩個(gè)值的大?。海?）SKIPIF1<0，SKIPIF1<0；（2）SKIPIF1<0，SKIPIF1<0；（3）SKIPIF1<0，SKIPIF1<0.例6、已知SKIPIF1<0，比較SKIPIF1<0，SKIPIF1<0的大小。例7、求函數(shù)SKIPIF1<0的單調(diào)區(qū)間。練習(xí)7、比較下列比較下列各組數(shù)中兩個(gè)值的大?。海?）SKIPIF1<0，SKIPIF1<0；（2）SKIPIF1<0，SKIPIF1<0；（3）SKIPIF1<0，SKIPIF1<0，SKIPIF1<0；（4）SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．練習(xí)8、若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是增函數(shù)，SKIPIF1<0的取值范圍?？键c(diǎn)六、函數(shù)的奇偶性例8、判斷函數(shù)SKIPIF1<0的奇偶性。練習(xí)9、（1）函數(shù)SKIPIF1<0的奇偶性是。（2）函數(shù)SKIPIF1<0的奇偶性為【課后練習(xí)】選擇題：1、已知SKIPIF1<0，那么SKIPIF1<0用SKIPIF1<0表示是（）A、SKIPIF1<0B、SKIPIF1<0C、SKIPIF1<0D、SKIPIF1<02、SKIPIF1<0，則SKIPIF1<0的值為（）A、SKIPIF1<0B、4C、1D、4或13、若SKIPIF1<0，則SKIPIF1<0的值為（）A1B2C3D44、如果方程SKIPIF1<0的兩根是SKIPIF1<0，則SKIPIF1<0的值是（）A、SKIPIF1<0B、SKIPIF1<0C、35D、SKIPIF1<05、已知SKIPIF1<0，那么SKIPIF1<0等于（）A、SKIPIF1<0B、SKIPIF1<0C、SKIPIF1<0D、SKIPIF1<06、函數(shù)SKIPIF1<0的圖像關(guān)于（）A、SKIPIF1<0軸對(duì)稱B、SKIPIF1<0軸對(duì)稱C、原點(diǎn)對(duì)稱D、直線SKIPIF1<0對(duì)稱7、函數(shù)SKIPIF1<0的定義域是（）A、SKIPIF1<0B、SKIPIF1<0C、SKIPIF1<0D、SKIPIF1<08、函數(shù)SKIPIF1<0的值域是（）A、SKIPIF1<0B、SKIPIF1<0C、SKIPIF1<0D、SKIPIF1<09、若SKIPIF1<0，那么SKIPIF1<0滿足的條件是（）A、SKIPIF1<0B、SKIPIF1<0C、SKIPIF1<0D、SKIPIF1<010、SKIPIF1<0，則SKIPIF1<0的取值范圍是（）A、SKIPIF1<0B、SKIPIF1<0C、SKIPIF1<0D、SKIPIF1<011、下列函數(shù)中，在SKIPIF1<0上為增函數(shù)的是（）A、SKIPIF1<0B、SKIPIF1<0C、SKIPIF1<0D、SKIPIF1<012、已知SKIPIF1<0在SKIPIF1<0上有SKIPIF1<0，則SKIPIF1<0是（）A、在SKIPIF1<0上是增加的B、在SKIPIF1<0上是減少的C、在SKIPIF1<0上是增加的D、在SKIPIF1<0上是減少的填空題13、若SKIPIF1<0。14、函數(shù)SKIPIF1<0的定義域是。15、SKIPIF1<0。16、函數(shù)SKIPIF1<0是（奇、偶）函數(shù)。三、解答題：（本題共3小題，共36分，解答應(yīng)寫出文字說明，證明過程或演算步驟.）17、已知函數(shù)SKIPIF1<0，判斷SKIPIF1<0的奇偶性和單調(diào)性。18、已知函數(shù)SKIPIF1<0，(1)求SKIPIF1<0的定義域；(2)判斷SKIPIF1<0的奇偶性。19、設(shè)函數(shù)SKIPIF1<0且SKIPIF1<0求a,b的值；當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0最大值20、已知函數(shù)SKIPIF1<0在定義域SKIPIF1<0上是減函數(shù)，且SKIPIF1<0求a的取值范圍；解不等式：SKIPIF1<0冪函數(shù)總復(fù)習(xí)【知識(shí)點(diǎn)回顧】（1）冪函數(shù)的定義一般地，函數(shù)SKIPIF1<0叫做冪函數(shù)，其中SKIPIF1<0為自變量，SKIPIF1<0是常數(shù)．（2）冪函數(shù)的圖象（3）冪函數(shù)的性質(zhì)①圖象分布：冪函數(shù)圖象分布在第一、二、三象限，第四象限無圖象．冪函數(shù)是偶函數(shù)時(shí)，圖象分布在第一、二象限(圖象關(guān)于SKIPIF1<0軸對(duì)稱)；是奇函數(shù)時(shí)，圖象分布在第一、三象限(圖象關(guān)于原點(diǎn)對(duì)稱)；是非奇非偶函數(shù)時(shí)，圖象只分布在第一象限．②過定點(diǎn)：所有的冪函數(shù)在SKIPIF1<0都有定義，并且圖象都通過點(diǎn)SKIPIF1<0．③單調(diào)性：如果SKIPIF1<0，則冪函數(shù)的圖象過原點(diǎn)，并且在SKIPIF1<0上為增函數(shù)．如果SKIPIF1<0，則冪函數(shù)的圖象在SKIPIF1<0上為減函數(shù)，在第一象限內(nèi)，圖象無限接近SKIPIF1<0軸與SKIPIF1<0軸．④奇偶性：當(dāng)SKIPIF1<0為奇數(shù)時(shí)，冪函數(shù)為奇函數(shù)，當(dāng)SKIPIF1<0為偶數(shù)時(shí)，冪函數(shù)為偶函數(shù)．當(dāng)SKIPIF1<0（其中SKIPIF1<0互質(zhì)，SKIPIF1<0和SKIPIF1<0），若SKIPIF1<0為奇數(shù)SKIPIF1<0為奇數(shù)時(shí)，則SKIPIF1<0是奇函數(shù)，若SKIPIF1<0為奇數(shù)SKIPIF1<0為偶數(shù)時(shí)，則SKIPIF1<0是偶函數(shù)，若SKIPIF1<0為偶數(shù)SKIPIF1<0為奇數(shù)時(shí)，則SKIPIF1<0是非奇非偶函數(shù)．⑤圖象特征：冪函數(shù)SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，