1/13集合一、集合的概念1．已知集合A={1，2，3，4}，那么A的真子集的個(gè)數(shù)是（）A．15 B．16 C．3 D．42．設(shè)集合SKIPIF1<0，若SKIPIF1<0，則下列關(guān)系正確的是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<03.下列四個(gè)集合中，是空集的是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<04.設(shè)集合A＝{x|x＝5－4a＋a2，a∈R}，B＝{y|y＝4b2＋4b＋2，b∈R}，則下列關(guān)系式中正確的是 ( )5.設(shè)M={x|x2+x+2=0}，a=lg(lg10)，則{a}與M的關(guān)系是 （）A、{a}=MB、MSKIPIF1<0{a}C、{a}SKIPIF1<0MD、MSKIPIF1<0{a}二、集合的性質(zhì)SKIPIF1<0設(shè)集合P={3，4，5}，Q={4，5，6，7}，定義P★Q={（SKIPIF1<0則P★Q中元素的個(gè)數(shù)為個(gè)三、集合的運(yùn)算8.SKIPIF1<09.SKIPIF1<010.已知集合A={x|x2-3x+2=0}，B={x|x2-mx+2=0}，且A∩B=B，求實(shí)數(shù)m范圍。11.SKIPIF1<0若SKIPIF1<0若SKIPIF1<0SKIPIF1<012.記函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，函數(shù)SKIPIF1<0,SKIPIF1<0的定義域?yàn)镾KIPIF1<0（Ⅰ）求SKIPIF1<0、SKIPIF1<0；（Ⅱ）若SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍.13.設(shè)集合A={x||x－a|<2}，B={x|SKIPIF1<0<1}，若ASKIPIF1<0B，求實(shí)數(shù)a的取值范圍。四、韋恩圖14.在100個(gè)學(xué)生中，有乒乓球愛(ài)好者60人，排球愛(ài)好者65人，則兩者都愛(ài)好的人數(shù)最少是________人。15.某班共30人，其中15人喜愛(ài)宮崎駿的漫畫(huà)，10人喜愛(ài)柯南，8人對(duì)這兩種都不喜愛(ài)，則喜愛(ài)宮崎駿的漫畫(huà)但不喜愛(ài)柯南的人數(shù)為16.向50名學(xué)生調(diào)查對(duì)A、B兩事件的態(tài)度，有如下結(jié)果贊成A的人數(shù)是全體的五分之三，其余的不贊成，贊成B的比贊成A的多3人，其余的不贊成；另外，對(duì)A、B都不贊成的學(xué)生數(shù)比對(duì)A、B都贊成的學(xué)生數(shù)的三分之一多1人。問(wèn)對(duì)A、B都贊成的學(xué)生和都不贊成的學(xué)生各有多少人？五、集合的運(yùn)用17.下列命題中的假命題是A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<018.已知a>0，則x0滿足關(guān)于x的方程ax=b的充要條件是(A)SKIPIF1<0(B)SKIPIF1<0(C)SKIPIF1<0(D)SKIPIF1<0六、二次函數(shù)已知關(guān)于的不等式的解集為,求的解集.22.關(guān)于SKIPIF1<0的不等式(SKIPIF1<0SKIPIF1<0-1)(SKIPIF1<0-2)＞0，若此不等式的解集為{SKIPIF1<0|＜x＜2}，則SKIPIF1<0的取值范圍是A.SKIPIF1<0＞0

B.0＜SKIPIF1<0＜2

C.SKIPIF1<0＞

D.SKIPIF1<0＜023.不等式（SKIPIF1<0－2）SKIPIF1<02+2(SKIPIF1<0－2)x-4＜0,對(duì)一切SKIPIF1<0∈R恒成立，則a的取值范圍是（

）A.（-∞,2]

B.（-2,2]

C.（-2,2）

D.（-∞,2)函數(shù)定義域與解析式一、函數(shù)定義域1.（1）求SKIPIF1<0的定義域；(2)已知SKIPIF1<0的定義域?yàn)镾KIPIF1<0，求SKIPIF1<0的定義域.2.設(shè)SKIPIF1<0，則SKIPIF1<0的定義域?yàn)椋ǎ㏒KIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<03.SKIPIF1<04.已知函數(shù)f（x）=SKIPIF1<0的定義域是R，則實(shí)數(shù)a的取值范圍是（）A．a(chǎn)＞SKIPIF1<0 B．－12＜a≤0 C．－12＜a＜0 D．a(chǎn)≤SKIPIF1<05.SKIPIF1<0已知函數(shù)SKIPIF1<0的定義域?yàn)镽，則SKIPIF1<0的范圍為已知函數(shù)SKIPIF1<0的值域?yàn)镽，則SKIPIF1<0的范圍為8.已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，則SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0（）二、解析式9.設(shè)SKIPIF1<0（）A．0B．1C．2D．310.設(shè)函數(shù)SKIPIF1<011.已知函數(shù)SKIPIF1<0是在SKIPIF1<0上的奇函數(shù)，函數(shù)SKIPIF1<0是在SKIPIF1<0上的偶函數(shù)，且SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0的值為（）SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<012.設(shè)函數(shù)f（x）＝SKIPIF1<0，則滿足f（x）=SKIPIF1<0的x值為。13.設(shè)SKIPIF1<0則不等式SKIPIF1<0的解集為（）A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<014.對(duì)任意的兩個(gè)實(shí)數(shù)對(duì)SKIPIF1<0和SKIPIF1<0，規(guī)定：SKIPIF1<0當(dāng)且僅當(dāng)SKIPIF1<0；運(yùn)算“SKIPIF1<0”為：SKIPIF1<0；運(yùn)算“SKIPIF1<0”為：SKIPIF1<0.設(shè)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0等于（）SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<015.求下列函數(shù)解析式：(1)已知SKIPIF1<0，求SKIPIF1<0；（2）已知SKIPIF1<0，求SKIPIF1<0；（3）已知SKIPIF1<0，求SKIPIF1<0.SKIPIF1<017設(shè)f（x）是定義在R上的奇函數(shù)，若當(dāng)x≥0時(shí)，f（x）=log3（1+x），則f（－2）=已知定義在R上的函數(shù)y=f(x)滿足f(2+x)=f(2－x)，且f(x)是偶函數(shù)，當(dāng)x∈[0，2]時(shí)，f(x)=2x－1，求x∈[－4，0]時(shí)f(x)的表達(dá)式。19.已知函數(shù)SKIPIF1<0，那么SKIPIF1<0函數(shù)的奇偶性和單調(diào)性一、奇偶性1.判斷下列函數(shù)的奇偶性：（1）SKIPIF1<0；（2）SKIPIF1<0；2.設(shè)SKIPIF1<0是奇函數(shù)，則使SKIPIF1<0的SKIPIF1<0的取值范圍是（）SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<03.SKIPIF1<04.已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0是奇函數(shù).（1）求SKIPIF1<0的解析式；（2）若對(duì)SKIPIF1<0，對(duì)任意的SKIPIF1<0，SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍.二、單調(diào)性5.設(shè)SKIPIF1<0，定義在區(qū)間SKIPIF1<0內(nèi)的函數(shù)SKIPIF1<0是奇函數(shù)。（1）求SKIPIF1<0的取值范圍（2）討論函數(shù)SKIPIF1<0的單調(diào)性6.SKIPIF1<0___SKIPIF1<08.已知函數(shù)SKIPIF1<0，若SKIPIF1<0在區(qū)間SKIPIF1<0上是減函數(shù)，則實(shí)數(shù)SKIPIF1<0的取值范圍是.9.已知SKIPIF1<0是SKIPIF1<0上的減函數(shù)，那么SKIPIF1<0的取值范圍是（）SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<010.設(shè)SKIPIF1<0是連續(xù)的偶函數(shù)，且當(dāng)SKIPIF1<0時(shí)SKIPIF1<0是單調(diào)函數(shù)，則滿足SKIPIF1<0的所有SKIPIF1<0之和為（）SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<011.已知偶函數(shù)f(x)在(0，+∞)上為增函數(shù)，且f(2)=0，解不等式f［log2(x2+5x+4)］≥0。函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，且在SKIPIF1<0上為增函數(shù)，若SKIPIF1<0，求SKIPIF1<0的取值范圍.13.已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且單調(diào)遞減，若SKIPIF1<0，求SKIPIF1<0的取值范圍.SKIPIF1<0（1）SKIPIF1<0（2）SKIPIF1<015．已知函數(shù)SKIPIF1<0對(duì)任意SKIPIF1<0，都有SKIPIF1<0SKIPIF1<0（1）求SKIPIF1<0 （2）證明SKIPIF1<0是R上的減函數(shù)16.函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間是.函數(shù)的圖像及值域一、函數(shù)的對(duì)稱(chēng)性、周期性1.在SKIPIF1<0上定義的函數(shù)SKIPIF1<0是偶函數(shù)，且SKIPIF1<0.若SKIPIF1<0在區(qū)間SKIPIF1<0上是減函數(shù)，則SKIPIF1<0（）SKIPIF1<0.在區(qū)間SKIPIF1<0上是增函數(shù)，在區(qū)間SKIPIF1<0上是增函數(shù)SKIPIF1<0.在區(qū)間SKIPIF1<0上時(shí)增函數(shù)，在區(qū)間SKIPIF1<0上是減函數(shù)SKIPIF1<0.在區(qū)間SKIPIF1<0上是減函數(shù)，在區(qū)間SKIPIF1<0上是增函數(shù)SKIPIF1<0.在區(qū)間SKIPIF1<0上是減函數(shù)，在區(qū)間SKIPIF1<0上是減函數(shù)2.已知定義域?yàn)镾KIPIF1<0的函數(shù)SKIPIF1<0在SKIPIF1<0上為減函數(shù)，且函數(shù)SKIPIF1<0為偶函數(shù)，則（）SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<03.已知定義在R上的函數(shù)y=f(x)滿足f(2+x)=f(2－x)，且f(x)是偶函數(shù)，當(dāng)x∈[0，2]時(shí)，f(x)=2x－1，求x∈[－4，0]時(shí)f(x)的表達(dá)式。4.已知SKIPIF1<0是偶函數(shù)，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)SKIPIF1<0為增函數(shù)，若SKIPIF1<0，且SKIPIF1<0，則（）SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<05.SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0設(shè)SKIPIF1<0為SKIPIF1<0上的奇函數(shù)，且SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的取值范圍是.函數(shù)SKIPIF1<0對(duì)于任意實(shí)數(shù)SKIPIF1<0滿足條件SKIPIF1<0，若SKIPIF1<0則SKIPIF1<08.若函數(shù)SKIPIF1<0、SKIPIF1<0分別為SKIPIF1<0上的奇函數(shù)、偶函數(shù)，且滿足SKIPIF1<0，則有（）A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<0二、函數(shù)圖像及變換9．函數(shù)y=1－SKIPIF1<0的圖象是（）SKIPIF1<010．函數(shù)SKIPIF1<0與SKIPIF1<0的圖像如下圖：則函數(shù)SKIPIF1<0的圖像可能是（）11．在下列圖象中，二次函數(shù)y=ax2+bx與指數(shù)函數(shù)y=（SKIPIF1<0）x的圖象只可能是（）SKIPIF1<012.將函數(shù)SKIPIF1<0的圖象按向量SKIPIF1<0平移得到函數(shù)SKIPIF1<0的圖象，則（）A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<013.函數(shù)SKIPIF1<0的圖像與函數(shù)SKIPIF1<0的圖像關(guān)于（）點(diǎn)SKIPIF1<0對(duì)稱(chēng)B.直線SKIPIF1<0對(duì)稱(chēng)C.點(diǎn)SKIPIF1<0對(duì)稱(chēng)D.直線SKIPIF1<0對(duì)稱(chēng)三、函數(shù)值域1）常見(jiàn)函數(shù)14.SKIPIF1<0SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<015.函數(shù)SKIPIF1<0的值域是16.函數(shù)SKIPIF1<0SKIPIF1<0且SKIPIF1<0在SKIPIF1<0上的最大值比最小值大SKIPIF1<0，則SKIPIF1<0的值是.17.設(shè)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0則SKIPIF1<0的最大值為.18.SKIPIF1<019.若函數(shù)SKIPIF1<0的值域是SKIPIF1<0，則函數(shù)SKIPIF1<0的值域是（）SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<02）換元法20.已知函數(shù)SKIPIF1<0的最大值為SKIPIF1<0，最小值為SKIPIF1<0，則SKIPIF1<0的值為（）SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<021.已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的值域?yàn)椋ǎ㏒KIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<021.已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的值域?yàn)椋ǎ㏒KIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0SKIPIF1<0.SKIPIF1<0參數(shù)分離22.SKIPIF1<0時(shí)，SKIPIF1<0函數(shù)與方程一、函數(shù)零點(diǎn)與方程的解1．若SKIPIF1<0，則方程SKIPIF1<0的根是() A．SKIPIF1<0 B．－SKIPIF1<0 C．2 D．－22.設(shè)函數(shù)SKIPIF1<0對(duì)SKIPIF1<0都滿足SKIPIF1<0,且方程SKIPIF1<0恰有6個(gè)不同的實(shí)數(shù)根，則這6個(gè)實(shí)根的和為（）A．0B．9C．12D．183.若關(guān)于SKIPIF1<0的方程SKIPIF1<0有解，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<04.方程SKIPIF1<0有解，則SKIPIF1<0的最小值為（）A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<05.SKIPIF1<06.SKIPIF1<0（1）有兩個(gè)零點(diǎn)且兩個(gè)零點(diǎn)分別位于SKIPIF1<0的異側(cè)；（2）有兩個(gè)零點(diǎn)且兩個(gè)零點(diǎn)位于區(qū)間SKIPIF1<0內(nèi)。7.若關(guān)于SKIPIF1<0