新高考數(shù)學(xué)一輪復(fù)習(xí)專題二函數(shù)及其性質(zhì)2-1函數(shù)的概念和基本性質(zhì)練習(xí)含答案

專題二函數(shù)及其性質(zhì)2.1函數(shù)的概念和基本性質(zhì)五年高考高考新風(fēng)向1.(概念深度理解)(2024新課標(biāo)Ⅰ,6,5分,中)已知函數(shù)f(x)=?x2?2ax?a,x<0,ex+ln(xA.(-∞,0]B.[-1,0]C.[-1,1]D.[0,+∞)2.(創(chuàng)新考法)(2024新課標(biāo)Ⅱ,8,5分,中)設(shè)函數(shù)f(x)=(x+a)·ln(x+b).若f(x)≥0,則a2+b2的最小值為(C)A.18B.14C.13.(創(chuàng)新考法)(2024新課標(biāo)Ⅱ,6,5分,中)設(shè)函數(shù)f(x)=a(x+1)2-1,g(x)=cosx+2ax.當(dāng)x∈(-1,1)時(shí),曲線y=f(x)與y=g(x)恰有一個(gè)交點(diǎn).則a=(D)A.-1B.12C.1D.24.(創(chuàng)新考法)(2024新課標(biāo)Ⅰ,8,5分,中)已知函數(shù)f(x)的定義域?yàn)镽,f(x)>f(x-1)+f(x-2),且當(dāng)x<3時(shí),f(x)=x,則下列結(jié)論中一定正確的是(B)A.f(10)>100B.f(20)>1000C.f(10)<1000D.f(20)<10000考點(diǎn)1函數(shù)的單調(diào)性與最值1.(2021全國(guó)甲文,4,5分,易)下列函數(shù)中是增函數(shù)的為(D)A.f(x)=-xB.f(x)=2C.f(x)=x2D.f(x)=32.(2023新課標(biāo)Ⅰ,4,5分,易)設(shè)函數(shù)f(x)=2x(x-a)在區(qū)間(0,1)單調(diào)遞減,則a的取值范圍是(D)A.(-∞,-2]B.[-2,0)C.(0,2]D.[2,+∞)3.(2020新高考Ⅱ,7,5分,中)已知函數(shù)f(x)=lg(x2-4x-5)在(a,+∞)單調(diào)遞增,則a的取值范圍是(D)A.(-∞,-1]B.(-∞,2]C.[2,+∞)D.[5,+∞)4.(2023全國(guó)甲文,11,5分,中)已知函數(shù)f(x)=e?(x?1)2.記a=f22,b=f32,c=f62A.b>c>aB.b>a>cC.c>b>aD.c>a>b5.(2020新高考Ⅰ,8,5分,難)若定義在R的奇函數(shù)f(x)在(-∞,0)單調(diào)遞減,且f(2)=0,則滿足xf(x-1)≥0的x的取值范圍是(D)A.[-1,1]∪[3,+∞)B.[-3,-1]∪[0,1]C.[-1,0]∪[1,+∞)D.[-1,0]∪[1,3]考點(diǎn)2函數(shù)的奇偶性1.(2023全國(guó)乙,文5,理4,5分,中)已知f(x)=xexeax?1是偶函數(shù),則a=(A.-2B.-1C.1D.22.(2023新課標(biāo)Ⅱ,4,5分,易)若f(x)=(x+a)·ln2x?12x+1為偶函數(shù),則a=(A.-1B.0C.123.(2021全國(guó)乙理,4,5分,中)設(shè)函數(shù)f(x)=1?x1+x,則下列函數(shù)中為奇函數(shù)的是(BA.f(x-1)-1B.f(x-1)+1C.f(x+1)-1D.f(x+1)+14.(2020課標(biāo)Ⅱ文,10,5分,中)設(shè)函數(shù)f(x)=x3-1x3,則f(x)(AA.是奇函數(shù),且在(0,+∞)單調(diào)遞增B.是奇函數(shù),且在(0,+∞)單調(diào)遞減C.是偶函數(shù),且在(0,+∞)單調(diào)遞增D.是偶函數(shù),且在(0,+∞)單調(diào)遞減5.(2020課標(biāo)Ⅱ理,9,5分,中)設(shè)函數(shù)f(x)=ln|2x+1|-ln|2x-1|,則f(x)(D)A.是偶函數(shù),且在12B.是奇函數(shù),且在?1C.是偶函數(shù),且在?∞D(zhuǎn).是奇函數(shù),且在?∞6.(2023全國(guó)甲,文14,理13,5分,易)若f(x)=(x-1)2+ax+sinx+π2為偶函數(shù),則a=7.(2021新高考Ⅰ,13,5分,易)已知函數(shù)f(x)=x3(a·2x-2-x)是偶函數(shù),則a=1.

8.(2022全國(guó)乙文,16,5分,中)若f(x)=lna+11?x+b是奇函數(shù),則a=-12,9.(2021新高考Ⅱ,14,5分,中)寫出一個(gè)同時(shí)具有下列性質(zhì)①②③的函數(shù)f(x):f(x)=x4(x∈R)(答案不唯一).

①f(x1x2)=f(x1)f(x2);②當(dāng)x∈(0,+∞)時(shí),f'(x)>0;③f'(x)是奇函數(shù).考點(diǎn)3函數(shù)的周期性和對(duì)稱性1.(2021新高考Ⅱ,8,5分,中)設(shè)函數(shù)f(x)的定義域?yàn)镽,且f(x+2)為偶函數(shù),f(2x+1)為奇函數(shù),則(B)A.f?12=0B.f(-1C.f(2)=0D.f(4)=02.(2021全國(guó)甲理,12,5分,難)設(shè)函數(shù)f(x)的定義域?yàn)镽,f(x+1)為奇函數(shù),f(x+2)為偶函數(shù),當(dāng)x∈[1,2]時(shí),f(x)=ax2+b.若f(0)+f(3)=6,則f92=(D)A.-94B.-32C.743.(2022新高考Ⅱ,8,5分,難)已知函數(shù)f(x)的定義域?yàn)镽,且f(x+y)+f(x-y)=f(x)f(y),f(1)=1,則k=122f(k)=(AA.-3B.-2C.0D.14.(2022全國(guó)乙理,12,5分,難)已知函數(shù)f(x),g(x)的定義域均為R,且f(x)+g(2-x)=5,g(x)-f(x-4)=7.若y=g(x)的圖象關(guān)于直線x=2對(duì)稱,g(2)=4,則k=122f(k)=(DA.-21B.-22C.-23D.-245.(多選)(2023新課標(biāo)Ⅰ,11,5分,中)已知函數(shù)f(x)的定義域?yàn)镽,f(xy)=y2f(x)+x2f(y),則(ABC)A.f(0)=0B.f(1)=0C.f(x)是偶函數(shù)D.x=0為f(x)的極小值點(diǎn)6.(多選)(2022新高考Ⅰ,12,5分,難)已知函數(shù)f(x)及其導(dǎo)函數(shù)f'(x)的定義域均為R,記g(x)=f'(x).若f32?2x,g(2+x)均為偶函數(shù),則(A.f(0)=0B.g?1C.f(-1)=f(4)D.g(-1)=g(2)

三年模擬練速度1.(2024東北三省三校第一次聯(lián)合模擬,3)已知函數(shù)y=f(x)是定義在R上的奇函數(shù),且當(dāng)x<0時(shí),f(x)=x2+ax,若f(3)=-8,則a=(B)A.-3B.3C.13D.-2.(2024河北唐山一模,4)已知函數(shù)f(x)=xx?2,則f(x)的最小值為(CA.0B.2C.22D.33.(2024江蘇南通第二次調(diào)研,4)已知函數(shù)f(x)=2x+2?x,x≤3,fx2,x>3,A.83B.103C.8094.(2024浙江金麗衢十二校第二次聯(lián)考,3)若函數(shù)f(x)=ln(ex+1)+ax為偶函數(shù),則實(shí)數(shù)a的值為(A)A.-12B.0C.125.(2024湖北T8聯(lián)盟模擬,6)已知函數(shù)f(x)=xlgx+bx+a(a≠b)為偶函數(shù),若b>1,則a不可能為(A.-2024B.-2C.-2D.-16.(2024福建福州質(zhì)檢,5)若函數(shù)f(x)=3|a-2x|在區(qū)間(1,2)上單調(diào)遞減,則a的取值范圍是(D)A.(-∞,2]B.(-∞,4]C.[2,+∞)D.[4,+∞)7.(2024江蘇宿遷調(diào)研測(cè)試,7)已知定義在R上的奇函數(shù)f(x)滿足f(2-x)=f(x),當(dāng)0≤x≤1時(shí),f(x)=2x-1,則f(log212)=(A)A.-13B.-14C.138.(2024湖南常德模擬,3)已知奇函數(shù)y=f(x)是定義域?yàn)镽的連續(xù)函數(shù),且在區(qū)間(0,+∞)上單調(diào)遞增,則下列說(shuō)法正確的是(C)A.函數(shù)y=f(x)+x2在R上單調(diào)遞增B.函數(shù)y=f(x)-x2在(0,+∞)上單調(diào)遞增C.函數(shù)y=x2f(x)在R上單調(diào)遞增D.函數(shù)y=f(x)x2在(9.(2024廣東茂名一模,6)函數(shù)y=f(x)和y=f(x-2)均為R上的奇函數(shù),若f(1)=2,則f(2023)=(A)A.-2B.-1C.0D.210.(2024山東菏澤一模,6)已知f(x)=xh(x),其中h(x)是奇函數(shù)且在R上為增函數(shù),則(C)A.flog213>f(2?32B.f(2?32)>f(2?C.flog213>f(2?23D.f(2?23)>f(2?11.(2024遼寧沈陽(yáng)育才中學(xué)模擬,7)函數(shù)y=xf(x)是定義在R上的奇函數(shù),且f(x)在區(qū)間[0,+∞)上單調(diào)遞增,若關(guān)于實(shí)數(shù)t的不等式f(log3t)+f(log13t)>2f(2)恒成立,則t的取值范圍是(DA.0,13∪(3,+∞)C.(9,+∞)D.0,19∪(9,12.(2024安徽皖江名校聯(lián)盟二模,8)已知函數(shù)y=f(x)(x≠0)滿足f(xy)=f(x)+f(y)-1,當(dāng)x>1時(shí),f(x)<1,則(C)A.f(x)為奇函數(shù)B.若f(2x+1)>1,則-1<x<0C.若f(2)=12,則f(1024)D.若f12=2,則f113.(2024貴州黔東南二模,14)若f(x)為定義在R上的偶函數(shù),且f(2x-3)為奇函數(shù),f(2)=1,則f(3)+f(8)=-1.

14.(2024湖北十一校第二次聯(lián)考,12)已知函數(shù)f(x)=x+1,x≤0,ln(x+1),x>0,則關(guān)于x的不等式f(x)≤1的解集為15.(2024山東聊城一模,13)若函數(shù)f(x)=6a?x,x≤4,log2x,x>4的值域?yàn)?2,練思維1.(2024廣西柳州三模,8)設(shè)函數(shù)f(x)是定義在R上的奇函數(shù),且對(duì)于任意不相等的x,y∈R,都有|f(x)-f(y)|<|x-y|.若函數(shù)g(x)-f(x)=x,則不等式g(2x-x2)+g(x-2)<0的解集是(D)A.(-1,2)B.(1,2)C.(-∞,-1)∪(2,+∞)D.(-∞,1)∪(2,+∞)2.(2024安徽A10聯(lián)盟質(zhì)量檢測(cè),8)若定義在R上的函數(shù)f(x),滿足2f(x+y)f(x-y)=f(2x)+f(2y),且f(1)=-1,則f(0)+f(1)+f(2)+…+f(2024)=(D)A.0B.-1C.2D.13.(2024浙江溫州二模,8)已知定義在(0,1)上的函數(shù)f(x)=1n,x是有理數(shù)mn(mA.f(x)的圖象關(guān)于x=12B.f(x)的圖象關(guān)于12C.f(x)在(0,1)單調(diào)遞增D.f(x)有最小值4.(多選)(2024廣東一模,10)已知偶函數(shù)f(x)的定義域?yàn)镽,f12x+1為奇函數(shù),且f(x)在[0,1]上單調(diào)遞增,則下列結(jié)論正確的是(BDA.f?32<0B.f4C.f(3)<0D.f202435.(多選)(2024山東齊魯名校聯(lián)盟聯(lián)考,9)已知函數(shù)f(x)的定義域?yàn)镽,f(2x+1)為奇函數(shù),f(4-x)=f(x),f(0)=2,且f(x)在[0,2]上單調(diào)遞減,則(ABD)A.f(1)=0B.f(8)=2C.f(x)在[6,8]上單調(diào)遞減D.f(x)在[0,100]上有50個(gè)零點(diǎn)6.(多選)(2024湖北新高考聯(lián)考協(xié)作體模擬(五),10)已知函數(shù)f(x)在R上可導(dǎo),且f(x)的導(dǎo)函數(shù)為g(x).若f(1)=1,f(x)+f(4-x)=0,g(2x+1)為奇函數(shù),則下列說(shuō)法正確的有(AD)A.f(x)是奇函數(shù)B.g(x)的圖象關(guān)于點(diǎn)?1C.f(2x+1)+f(1-2x)=0D.k=12024f(k7.(多選)(2024福建廈門第三次質(zhì)量檢測(cè),10)定義在R上的函數(shù)f(x)的值域?yàn)?-∞,0),且f(2x)+f(x+y)f(x-y)=0,則(ACD)A.f(0)=-1B.f(4)+f2(1)=0C.f(x)f(-x)=1D.f(x)+f(-x)≤-28.(多選)(2024浙江杭州二模,10)已知函數(shù)f(x)對(duì)任意實(shí)數(shù)x均滿足2f(x)+f(x2-1)=1,則(ACD)A.f(-x)=f(x)B.f(2)=1C.f(-1)=1D.函數(shù)f(x)在區(qū)間(2,3)上不單調(diào)9.(多選)(2024浙江麗水、湖州、衢州二模,11)已知函數(shù)f(x)的定義域?yàn)镽,且f(x+y)f(x-y)=f2(x)-f2(y),f(1)=2,f(x+1)為偶函數(shù),則(BCD)A.f(3)=2B.f(x)為奇函數(shù)C.f(2)=0D.k=12024f(k10.(多選)(2024福建莆田第二次教學(xué)質(zhì)量檢測(cè),11)已知定義在R上的函數(shù)f(x)滿足:f(x+y)=f(x)+f(y)-3xy(x+y),則(ABD)A.y=f(x)是奇函數(shù)B.若f(1)=1,則f(-2)=4C.若f(1)=-1,則y=f(x)+x3為增函數(shù)D.若?x>0,f(x)+x3>0,則y=f(x)+x3為增函數(shù)11.(多選)(2024安徽黃山第一次質(zhì)量檢測(cè),11)已知函數(shù)f(x)及其導(dǎo)函數(shù)f'(x)的定義域均為R,記g(x)=f'(x).若f(x)滿足f(2+3x)=f(-3x),g(x-2)的圖象關(guān)于直線x=2對(duì)稱,且g(0)=1,則(BCD)A.f(x)是奇函數(shù)B.g(1)=0C.f(x)=f(x+4)D.k=12024g12.(多選)(2024江蘇南通二調(diào),11)已知函數(shù)f(x),g(x)的定義域均為R,f(x)的圖象關(guān)于點(diǎn)(2,0)對(duì)稱,g(0)=g(2)=1,g(x+y)+g(x-y)=g(x)f(y),則(ACD)A.f(x)為偶函數(shù)B.g(x)為偶函數(shù)C.g(-1-x)=-g(-1+x)D.g(1-x)=g(1+x)練風(fēng)向(概念深度理解)(多選)(2024湖北七市州3月聯(lián)考,11)我們知道,函