高中數(shù)學(xué)必修一函數(shù)練習(xí)題

1、第1課 函數(shù)的概念【考點(diǎn)導(dǎo)讀】1.了解構(gòu)成函數(shù)的要素，會(huì)求一些簡(jiǎn)單函數(shù)的定義域和值域2.準(zhǔn)確理解函數(shù)的概念，能根據(jù)函數(shù)的三要素判斷兩個(gè)函數(shù)是否為同一函數(shù)【基礎(chǔ)練習(xí)】1設(shè)有函數(shù)組：，；，；，；，；，其中表示同一個(gè)函數(shù)的有_ y122xO122xyO122xOy2.設(shè)集合，從到有四種對(duì)應(yīng)如圖所示：122xOy其中能表示為到的函數(shù)關(guān)系的有_ 3.寫(xiě)出下列函數(shù)定義域：(1) 的定義域?yàn)開(kāi)； (2) 的定義域?yàn)開(kāi)；(3) 的定義域?yàn)開(kāi)； (4) 的定義域?yàn)開(kāi)4已知三個(gè)函數(shù):(1)； (2)； (3)寫(xiě)出使各函數(shù)式有意義時(shí)，的約束條件： (1)_(2)_； (3)_5.寫(xiě)出下列函數(shù)值域：(1) ，；值域是

2、(2) ； 值域是(3) ， 值域是【范例解析】例1.設(shè)有函數(shù)組：，；，；，；，其中表示同一個(gè)函數(shù)的有點(diǎn)評(píng)：兩個(gè)函數(shù)當(dāng)它們的三要素完全相同時(shí)，才能表示同一函數(shù)而當(dāng)一個(gè)函數(shù)定義域和對(duì)應(yīng)法則確定時(shí)，它的值域也就確定，故判斷兩個(gè)函數(shù)是否為同一函數(shù)，只需判斷它的定義域和對(duì)應(yīng)法則是否相同即可例2.求下列函數(shù)的定義域： ； ；例3.求下列函數(shù)的值域：（1），；（2）；（3）點(diǎn)評(píng)：二次函數(shù)或二次函數(shù)型的函數(shù)求值域可用配方法；逆求法利用函數(shù)有界性求函數(shù)的值域；用換元法求函數(shù)的值域應(yīng)注意新元的取值范圍【反饋演練】1函數(shù)f(x)的定義域是_2函數(shù)的定義域?yàn)開(kāi)3. 函數(shù)的值域?yàn)開(kāi)4. 函數(shù)的值域?yàn)開(kāi)5函數(shù)的定義域?yàn)?/p>

3、_【真題再現(xiàn)】1(2014山東)函數(shù)f(x) 的定義域?yàn)?)2（2014廣東）函數(shù)y的定義域是()3（2014遼寧）.已知函數(shù)f(x)ln(3x)1，則f(lg 2)f()4.（2013山東）函數(shù)f(x)log2(3x1)的值域?yàn)?)5.(2013浙江)已知函數(shù)f(x)= ,若f(a)=3,則實(shí)數(shù)a=.6.（2013天津）設(shè)函數(shù)g(x)x22(xR)，f(x)則f(x)的值域是(第2課 函數(shù)的表示方法【考點(diǎn)導(dǎo)讀】1.會(huì)根據(jù)不同的需要選擇恰當(dāng)?shù)姆椒ǎㄈ鐖D像法，列表法，解析法）表示函數(shù)2.求解析式一般有四種情況：（1）根據(jù)某個(gè)實(shí)際問(wèn)題須建立一種函數(shù)關(guān)系式；（2）給出函數(shù)特征，利用待定系數(shù)法求解析式

4、；（3）換元法求解析式；（4）解方程組法求解析式【基礎(chǔ)練習(xí)】1.設(shè)函數(shù)，則_；_2.設(shè)函數(shù)，,則_；第5題3.已知函數(shù)是一次函數(shù)，且，,則_4.設(shè)f(x)，則ff()_5.如圖所示的圖象所表示的函數(shù)解析式為_(kāi)【范例解析】例1.已知二次函數(shù)的最小值等于4，且，求的解析式分析：給出函數(shù)特征，可用待定系數(shù)法求解xyO1234102030405060例2例2.甲同學(xué)家到乙同學(xué)家的途中有一公園，甲從家到公園的距離與乙從家到公園的距離都是2km，甲10時(shí)出發(fā)前往乙家如圖，表示甲從出發(fā)到乙家為止經(jīng)過(guò)的路程y（km）與時(shí)間x（分）的關(guān)系試寫(xiě)出的函數(shù)解析式【反饋演練】1若，則（ ） 2.設(shè)x表示不大于x的最大整

5、數(shù), 則對(duì)任意實(shí)數(shù)x,有( )A .x=xB. x + =xC. 2x=2x D. 【真題再現(xiàn)】1.（2013北京已知函數(shù)(x) 若(a)(1)0，則實(shí)數(shù)a的值等于()2（2013北京）函數(shù)f(x)的值域?yàn)開(kāi)3.（2012福建）設(shè)f(x)g(x)則f(g()的值為4.（2010陜西）已知函數(shù)f(x)若f(f(0)4a，則實(shí)數(shù)a_.5.（2013福建）函數(shù)f(x)ln(x21)的圖像大致是()6.（2014江蘇）已知實(shí)數(shù)a0，函數(shù)f(x)若f(1a)f(1a)，則a的值為_(kāi)7.（2012江蘇）設(shè)f(x)是定義在R上且周期為2的函數(shù)，在區(qū)間1,1上，f(x)其中a，bR.若f()f()，則a3b的

6、值為_(kāi)第3課 函數(shù)的單調(diào)性【考點(diǎn)導(dǎo)讀】1.理解函數(shù)單調(diào)性，最大（?。┲导捌鋷缀我饬x；2.會(huì)運(yùn)用單調(diào)性的定義判斷或證明一些函數(shù)的增減性【基礎(chǔ)練習(xí)】1.下列函數(shù)中： ； ； ； 其中，在區(qū)間(0，2)上是遞增函數(shù)的序號(hào)有_2.函數(shù)的遞增區(qū)間是_ _3.已知函數(shù)在定義域R上是單調(diào)減函數(shù)，且，則實(shí)數(shù)a的取值范圍_4.已知下列命題：定義在上的函數(shù)滿足，則函數(shù)是上的增函數(shù)；定義在上的函數(shù)滿足，則函數(shù)在上不是減函數(shù)；定義在上的函數(shù)在區(qū)間上是增函數(shù)，在區(qū)間上也是增函數(shù)，則函數(shù)在上是增函數(shù)；定義在上的函數(shù)在區(qū)間上是增函數(shù)，在區(qū)間上也是增函數(shù)，則函數(shù)在上是增函數(shù)其中正確命題的序號(hào)有_【范例解析】1.下列函數(shù)中，既

7、是偶函數(shù)又在區(qū)間(0，)上單調(diào)遞減的是()Ay ByexCyx21 D. ylg|x|2.下列函數(shù)中，既是偶函數(shù)，又在區(qū)間(1,2)內(nèi)是增函數(shù)的為()Aycos 2x，xRBylog2|x|，xR且x0Cy，xRDyx31，xR【反饋演練】1已知函數(shù)，則該函數(shù)在上單調(diào)遞_，（填“增”“減”）值域?yàn)開(kāi)2已知函數(shù)在上是減函數(shù)，在上是增函數(shù)，則_.3. 函數(shù)的單調(diào)遞減區(qū)間為 【真題再現(xiàn)】1.（ 2011新課標(biāo)全國(guó)）下列函數(shù)中，既是偶函數(shù)又在(0，)單調(diào)遞增的函數(shù)是Ayx3 By|x|1 Cyx21 Dy2|x|2.(2009遼寧)已知偶函數(shù)f(x)在區(qū)間0，)單調(diào)增加，則滿足f(2x1)0時(shí)， f(

8、x) x2，則f(1)()2.（2011湖南）已知f(x)為奇函數(shù)，g(x)f(x)9，g(2)3，則f(2)_.3.（2010江蘇）設(shè)函數(shù)f(x)x(exaex)(xR)是偶函數(shù)，則實(shí)數(shù)a的值為_(kāi)4.，則 5已知函數(shù)滿足，且當(dāng) 時(shí)，則與 的圖象的交點(diǎn)個(gè)數(shù)為 .第5課 二次函數(shù)，冪函數(shù)，指對(duì)函數(shù)【考點(diǎn)導(dǎo)讀】1.理解二次函數(shù)的概念，掌握二次函數(shù)，冪函數(shù)，指對(duì)函數(shù)圖像和性質(zhì)；2.能結(jié)合二次函數(shù)的圖像判斷一元二次方程根的存在性及根的個(gè)數(shù)，從而了解函數(shù)的零點(diǎn)與方程根的聯(lián)系【基礎(chǔ)練習(xí)】1. 二次函數(shù)的圖像的對(duì)稱軸為,則_，遞增區(qū)間為_(kāi)，遞減區(qū)間為_(kāi)2. 實(shí)系數(shù)方程有兩正根的充要條件為_(kāi)；有兩負(fù)根的充要條

9、件為3. 已知函數(shù)在區(qū)間上有最大值3，最小值2，則m的取值范圍是_【范例解析】1. 已知a，b，cR，函數(shù)f(x)ax2bxc.若f(0)f(4)f(1)，則()Aa0,4ab0Ba0,2ab0 Daf(n)，則m、n的大小關(guān)系為_(kāi)6.已知函數(shù)過(guò)定點(diǎn)，則此定點(diǎn)坐標(biāo)為_(kāi)7函數(shù)上的最大值和最小值之和為a，則a的值為8函數(shù)對(duì)于任意的實(shí)數(shù)都有（ ）ABC D9.將y=2x的圖像 ( ) 再作關(guān)于直線y=x對(duì)稱的圖像，可得到函數(shù)的圖像A先向左平行移動(dòng)1個(gè)單位B先向右平行移動(dòng)1個(gè)單位1O11xy第10題C先向上平行移動(dòng)1個(gè)單位D 先向下平行移動(dòng)1個(gè)單位10函數(shù)的圖象如圖，其中a、b為常數(shù)，則下列結(jié)論正確的

10、是（ ）ABC D11函數(shù)在上的最大值與最小值的和為3，則的值為_(kāi)【反饋演練】1函數(shù)是單調(diào)函數(shù)的充要條件是2已知二次函數(shù)的圖像頂點(diǎn)為，且圖像在軸上截得的線段長(zhǎng)為8，則此二次函數(shù)的解析式為3. 設(shè)，二次函數(shù)的圖象為下列四圖之一： 則a的值為 （ ）A1B1CD【真題再現(xiàn)】1（2010山東）函數(shù)y2xx2的圖象大致是()2.(2013陜西)設(shè)a，b，c均為不等于1的正實(shí)數(shù)， 則下列等式中恒成立的是()AlogablogcblogcaBlogablogcalogcbCloga(bc)logablogacDloga(bc)logablogac3.（2010遼寧）設(shè)2a5bm，且2，則m()4（2012

11、北京）已知函數(shù)f(x)lg x，若f(ab)1，則f(a2)f(b2)_.5.（2011新課標(biāo)全國(guó)）已知函數(shù)yf(x)的周期為2，當(dāng)x1,1時(shí)f(x)x2，那么函數(shù)yf(x)的圖像與函數(shù)y|lgx|的圖像的交點(diǎn)共有()6(2009廣東)若函數(shù)yf(x)是函數(shù)yax(a0，且a1)的反函數(shù)，其圖象經(jīng)過(guò)點(diǎn)(，a)，則f(x)()第6課 函數(shù)與方程【考點(diǎn)導(dǎo)讀】1.能利用二次函數(shù)的圖像與判別式的正負(fù)，判斷一元二次方程根的存在性及根的個(gè)數(shù)，了解函數(shù)零點(diǎn)與方程根的聯(lián)系2.能借助計(jì)算器用二分法求方程的近似解，并理解二分法的實(shí)質(zhì)【基礎(chǔ)練習(xí)】1.函數(shù)在區(qū)間有_個(gè)零點(diǎn)2.已知函數(shù)的圖像是連續(xù)的，且與有如下的對(duì)應(yīng)值

12、表：1234562.33.401.33.43.4則在區(qū)間上的零點(diǎn)至少有_個(gè)【范例解析】1.函數(shù)f(x)=2x|log0.5x|-1的零點(diǎn)個(gè)數(shù)為()2.若abc,則函數(shù)f(x)=(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)兩個(gè)零點(diǎn)分別位于區(qū)間()A.(a,b)和(b,c)內(nèi) B.(-,a)和(a,b)內(nèi)C.(b,c)和(c,+)內(nèi) D.(-,a)和(c,+)內(nèi)3設(shè)函數(shù)若，則關(guān)于x的方程解的個(gè)數(shù)為（ ）【真題再現(xiàn)】1.（2011福建）若關(guān)于x的方程x2mx10有兩個(gè)不相等的實(shí)數(shù)根，則實(shí)數(shù)m的取值范圍是()A(1,1)B(2,2)C(，2)(2，) D(，1)(1，)2（2011

13、天津）對(duì)實(shí)數(shù)a和b，定義運(yùn)算“”：ab設(shè)函數(shù)f(x)(x22)(x1)，xR.若函數(shù)yf(x)c的圖像與x軸恰有兩個(gè)公共點(diǎn)，則實(shí)數(shù)c的取值范圍是()A(1,1(2，)B(2，1(1,2C(，2)(1,2D2，13.（2011陜西）方程|x|cosx在(，)內(nèi)()A沒(méi)有根 B有且僅有一個(gè)根C有且僅有兩個(gè)根 D有無(wú)窮多個(gè)根4. （2010福建）函數(shù)f(x)，的零點(diǎn)個(gè)數(shù)為()5（2014天津）函數(shù)f(x)exx2的零點(diǎn)所在的一個(gè)區(qū)間是()A(2，1) B(1,0)C(0,1) D(1,2)技術(shù)官員村位于位于亞運(yùn)城東部，主干道二以東石樓涌以西的地塊，占地面積、m2，總建筑面積、m2，共包括地下室南區(qū)、

14、地下室北區(qū)、地上部分1棟12棟、服務(wù)中心、室外工程等多個(gè)單體工程。其中住宅面積m2，共12棟，17棟建筑層數(shù)為11層，812棟11層（局部復(fù)式頂層），首層局部架空，布置公建配套設(shè)施。integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting

15、 deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply t

16、o the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and th

17、e second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-ci

18、ties in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. S

19、outhbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have be

20、en expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of i

21、ntegrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-

22、3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center