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版高考数学课时规范练7函数的奇偶性与周期性理北师大版41

课时规范练7 函数的奇偶性与周期性

基础巩固组

1.函数f(x)=-x的图像关于(  )

A.y轴对称B.直线y=-x对称

C.坐标原点对称D.直线y=x对称

2.(2018河北衡水中学月考,6)下列函数中,与函数y=-2x的定义域、单调性与奇偶性均一致的函数是(  )

A.y=sinxB.y=x2

C.y=D.y=

3.已知偶函数f(x)在区间[0,+∞)内递增,则满足f(2x-1)

A.B.

C.D.

4.(2018湖南长郡中学三模,6)已知f(x)为奇函数,函数f(x)与g(x)的图像关于直线y=x+1对称,若g

(1)=4,则f(-3)=(  )

A.-2B.2C.-1D.4

5.已知函数f(x)是定义在R上的奇函数,且满足f(x+2)=f(x).若当x∈[0,1)时,f(x)=2x-,则f(lo)的值为(  )

A.0B.1C.D.-

6.定义在R上的偶函数f(x)满足:

对任意的x1,x2∈(-∞,0)(x1≠x2),都有<0,则下列结论正确的是(  )

A.f(0.32)

B.f(log25)

C.f(log25)

D.f(0.32)

7.已知函数f(x)为奇函数,当x>0时,f(x)=x2-x,则当x<0时,函数f(x)的最大值为(  )

A.-B.

C.D.-

8.已知定义域为R的函数f(x)在(8,+∞)内为减函数,且函数y=f(x+8)为偶函数,则(  )

A.f(6)>f(7)B.f(6)>f(9)

C.f(7)>f(9)D.f(7)>f(10)

9.已知f(x)是定义在R上的偶函数,且f(x+4)=f(x-2).若当x∈[-3,0]时,f(x)=6-x,则f(919)=     . 

10.已知f(x)是奇函数,g(x)=,若g

(2)=3,则g(-2)=.

11.已知定义在R上的函数f(x),对任意实数x有f(x+4)=-f(x)+2,若函数f(x-1)的图像关于直线x=1对称,f(-1)=2,则f(2017)=     . 

综合提升组

12.(2018湖南长郡中学四模,9)下列函数既是奇函数又在(-1,1)上是减函数的是(  )

A.y=tanxB.y=x-1

C.y=lnD.y=(3x-3-x)

13.已知偶函数f(x)满足f(x)=x3-8(x≥0),则{x|f(x-2)>0}=(  )

A.{x|x<-2或x>4}

B.{x|x<0或x>4}

C.{x|x<0或x>6}

D.{x|x<-2或x>2}

14.已知奇函数f(x)的定义域为R,若f(x+1)为偶函数,且f

(1)=2,则f(4)+f(5)的值为(  )

A.2B.1

C.-1D.-2

15.已知定义在R上的奇函数f(x)满足:

f(x+1)=f(x-1),且当-1

A.B.-

C.-D.

创新应用组

16.(2018安徽宿州三模,8)已知函数y=f(x)为R上的偶函数,且满足f(x+2)=-f(x),当x∈[0,1]时,f(x)=1-x2.下列四个命题:

p1:

f

(1)=0;

p2:

2是函数y=f的一个周期;

p3:

函数y=f(x-1)在(1,2)上递增;

p4:

函数y=f(2x-1)的递增区间为,k∈Z.

其中真命题为(  )

A.p1,p2B.p2,p3C.p1,p4D.p2,p4

17.(2018河南六市联考一,12)已知定义在R上的奇函数f(x)满足:

f(x+2e)=-f(x)(其中e=2.718),且在区间[e,2e]上是减函数,令a=,b=,c=,则f(a),f(b),f(c)的大小关系为(  )

A.f(b)>f(a)>f(c)

B.f(b)>f(c)>f(a)

C.f(a)>f(b)>f(c)

D.f(a)>f(c)>f(b)

 

参考答案

 

课时规范练7 函数的奇偶性与周期性

1.C ∵f(-x)=-+x=-=-f(x),且定义域为(-∞,0)∪(0,+∞),

∴f(x)为奇函数.∴f(x)的图像关于坐标原点对称.

2.D 函数y=-2x的定义域为R,但在R上递减.

函数y=sinx和y=x2的定义域都为R,且在R上不单调,故不合题意;

函数y=的定义域为(-∞,0)∪(0,+∞),不合题意;

函数y=的定义域为R,且在R上递减,且奇偶性一致,故符合题意.故选D.

3.A 由于函数f(x)在区间[0,+∞)内递增,且f(x)为偶函数,则由f(2x-1)

4.A 由题意设P(1,4)关于y=x+1的对称点为P'(a,b),则解得则P'(3,2)在函数y=f(x)的图像上,故f(3)=2,则f(-3)=-2.故选A.

5.A 因为函数f(x)是定义在R上的奇函数,

所以f(lo4)=f(-log2)=f=-f.

又因为f(x+2)=f(x),

所以f=f=-=0.

所以f(lo4)=0.

6.A ∵对任意x1,x2∈(-∞,0),且x1≠x2,都有<0,∴f(x)在(-∞,0)内是减少的,又f(x)是R上的偶函数,

∴f(x)在(0,+∞)内是增函数.

∵0<0.32<20.3

∴f(0.32)

7.B 法一 设x<0,则-x>0,所以f(-x)=x2+x,又函数f(x)为奇函数,所以f(x)=-f(-x)=-x2-x=-+,所以当x<0时,函数f(x)的最大值为.故选B.

法二 当x>0时,f(x)=x2-x=-,最小值为-,因为函数f(x)为奇函数,所以当x<0时,函数f(x)的最大值为.故选B.

8.D 由y=f(x+8)为偶函数,知函数f(x)的图像关于直线x=8对称.

又因为f(x)在(8,+∞)内是减少的,所以f(x)在(-∞,8)内是增加的.可画出f(x)的草图(图略),知f(7)>f(10).

9.6 由f(x+4)=f(x-2)知,f(x)为周期函数,且周期T=6.

因为f(x)为偶函数,所以f(919)=f(153×6+1)=f

(1)=f(-1)=61=6.

10.-1 ∵g

(2)==3,∴f

(2)=1.

又f(-x)=-f(x),∴f(-2)=-1,

∴g(-2)===-1.

11.2 由函数y=f(x-1)的图像关于直线x=1对称可知,函数f(x)的图像关于y轴对称,故f(x)为偶函数.由f(x+4)=-f(x)+2,得f(x+4+4)=-f(x+4)+2=f(x),∴f(x)是周期T=8的偶函数,∴f(2017)=f(1+252×8)=f

(1)=f(-1)=2.

12.C y=tanx是奇函数,在(-1,1)上是增加的;y=x-1是奇函数,在(-1,0)上是减少的,在(0,1)上是减少的,y=ln=ln是奇函数且在(-1,1)上是减少的;y=(3x-3-x)是奇函数,在(-1,1)上是增加的;故选C.

13.B ∵f(x)是偶函数,∴f(x-2)>0等价于f(|x-2|)>0=f

(2).

∵f(x)=x3-8在[0,+∞)内是增加的,

∴|x-2|>2,解得x<0或x>4.

14.A ∵f(x+1)为偶函数,f(x)是奇函数,

∴f(-x+1)=f(x+1),f(x)=-f(-x),f(0)=0,

∴f(x+1)=f(-x+1)=-f(x-1),∴f(x+2)=-f(x),f(x+4)=f(x+2+2)=-f(x+2)=f(x),则f(4)=f(0)=0,f(5)=f

(1)=2,

∴f(4)+f(5)=0+2=2.故选A.

15.D 由f(x+1)=f(x-1),得f(x+2)=f[(x+1)+1]=f(x),∴f(x)是周期为2的周期函数.

∵log232>log220>log216,∴4

∵当x∈(-1,0)时,f(x)=2x-1,∴f=-,

故f(log220)=.

16.C ∵f(x+2)=-f(x),当x=-1时,f

(1)=-f(-1)=-f

(1),∴f

(1)=0,故p1正确;

∵f(x+2)=-f(x),∴f(x+4)=-f(x+2)=f(x),

∴y=f(x)的周期为4,y=f的周期为=8,故p2错;

∵当x∈[0,1]时,f(x)=1-x2,∴f(x)在区间[0,1]上递减,

∴函数y=f(x-1)在(1,2)上递减,故p3错;

∵当x∈[0,1]时,f(x)=1-x2,当x∈[-2,-1]时,x+2∈[0,1],

∴f(x)=-f(x+2)=-[1-(x+2)2]=(x+2)2-1,

∴f(x)在[-2,-1]递增,从而f(x)在[-2,0]递增,在[0,2]上递减,

又f(x)是周期为4的函数,

∴f(x)的增区间为[4k-2,4k],即4k-2≤2x-1≤4k,

∴2k-≤x≤2k+,

∴y=f(2x-1)的递增区间为,k∈Z,故p4正确,故选C.

17.A ∵f(x)是R上的奇函数,满足f(x+2e)=-f(x),∴f(x+2e)=f(-x),

∴f(x)的图像关于直线x=e对称,∵f(x)在区间[e,2e]上是减少的,∴f(x)在区间[0,e]上是增加的,

令y=,则y'=,

∴y=在(0,e]上递增,在(e,+∞)递减.∴b=>=c>0,

a-b=-==<0,a-c=-==>0,∴a>c.

∴0f(a)>f(c).

 

课时训练(九) Unit1(八下)

(限时:

30分钟)

Ⅰ.单项选择

1.—Doyourememberwhatshelookedlikewhenyoufirstmether?

—Ofcourse.Shewastallandthin    longhair. 

A.inB.withC.onD.by

2.[2018·苏州]—I'mgoingtomissyou,dear.

—Ifeel    thesame. 

A.hardlyB.exactly

C.seriouslyD.properly

3.[2018·黔南]Jackhaslearnedmoreaboutteamwork(团队合作)    hejoinedthesoccerteam. 

A.untilB.sinceC.whileD.though

4.[2018·贵港]—Manywildanimalsareingreatdanger.

—Let's    tosavethem. 

A.takeoffB.takedown

C.takeactionD.takeafter

5

.[2017·泰州]Dianausedto    towork,butnowsheisusedto    becausetheroadiscrowdedandshewantstokeepfit. 

A.drive;walkingB.drive;walk

C.driving;walkD.driving;walking

6.[2017·黔西南]HowdoesJane    withhermother?

    making

phonecallsorchattingonline?

 

A.keepintouch;WithB.keepingtouch;By

C.keepintouch;ByD.keepingtouch;With

7.Helen    Jeffwhentheywereboth25yearsold. 

A.gotmarriedtoB.gotmarriedwith

C.marriedwithD.marriedto

8.Mygrandmalives    inheroldhouse,butsheneverfeels    . 

A.lonely;lonelyB.alone;alone

C.lonely;aloneD.alone;lonely

9.[2018·日照]—Whenwillyougivethenovelbacktome?

—Sorry,I    it.HowaboutFriday?

 

A.didn'tfinishB.won'tfinish

C.haven'tfinishedD.don'tfinish

10.[2018·苏州模拟]Pickupyourpenanddrawyourowninvention.Maybeitwillbe    arealproductoneday!

 

A.turnedonB.turneddown

C.turnedintoD.turnedoff

Ⅱ.[2017·恩施]完形填空

HaveyoueverbeentoAmerica?

Iwasonlyan11-year-oldgirlwhenmyparents 11 methatwewouldsoonmovetoAmerica.Wewereonthebusthen.I

cried.IrememberthatIcouldnotbearthethoughtofneverhearing

theradioprogrammeforschoolchildrenagainwhichI 12 everymorning. 

  Infact,IthinkIcriedverylittlewhenIwassaying 13 tomyfriendsandrelatives.Whenwewereleaving,Ievenfeltalittle 14 becauseIthoughtaboutalltheplacesIwasgoingtosee—thestrangeand 15 placesIhadknownonlyfrombooksandpictures. 

  ThefirstfouryearsinAmericataughtmetheimportanceofoptimism(乐观),buttheideadidnotcometo 16 atonce.ForthefirsttwoyearsinNewYorkIwasreally 17 —havingtostudyinthreeschoolsandI 18 mostofmytimelearningtheEnglishlanguage.I 19 hadanytimeforfun.SometimesIdidnotquitekn

owwhatIwasorwhatIshouldbe.Mother 20 andthingsbecameevenharderforme.Ittook

me 21 togetusedtomystepfather.Iwasoften 22 ,andsawnoendto“thehardtimes”. 

  IhadtodomanythingsforthefamilysinceIknewEnglishbetterthaneveryoneelseathome.

   23 ,thingsgotbetterandbetterlaterandalmostallcommontroubles 24 atlast.FromthoseexperiencesIhavelearnedoneimportantrule:

Somethinggoodiscertaintohappenintheend 25 youdogiveup,andjustwaitalittle!

 

11.A.spokeB.said

C.toldD.announced

12.A.talkedaboutB.watched

C.studiedD.listenedto

13.A.sorryB.goodbye

C.helloD.thanks

14.A.upsetB.disappointed

C.afraidD.excited

15.A.magicalB.bori

ng

C.necessaryD.usual

16.A.himB.meC.herD.it

17.A.interestedB.happy

C.lostD.confident

18.A.wastedB.spentC.usedD.paid

19.A.hardlyB.hardC.nearlyD.always

20.A.returnedB.left

C.noticedD.remarried

21.A.sometimesB.somemoney

C.somewordsD.sometime

22.A.satisfiedB.sad

C.optimisticD.glad

23.A.EspeciallyB.Unfortunately

C.

ImmediatelyD.Luckily

24.A.wentawayB.wentup

C.wentalongD.wentover

25.A.toB.beforeC.wh

enD.unless

Ⅲ.[2019·原创]阅读理解

At9a.m.on21Sept.2017,ahigh-speedtrainleftBeijingforShanghai.Secondslater,whenthescreenshowedthespeedof350km/h,excitedpasseng

ershelduptheircamerasandcellphonesandtookphotosofit.China'snew-generationhigh-speedtrain,theFuxing,isnowoneofthefastesttrainsintheworld.

Bytheendof2017,therewere2,700high-speedtrainsrunningacrossChina,whichmadeup60percentoftheworld'stotalhigh-speedtrains.Chinahasbuiltmorethan10high-speedrailwaysinEurope,South-eastAsiaandSouthAmerica,andisquicklybecomingknownastheleaderofhigh-speedtraintechnol

ogy.

Besideshigh-speedrail,Chinahasimprovedpeople'slivesinmanyotherwaysoverthelasttenyears.Bikesharing,forexample,isnotnewitself.ButChinahasmadeitmuchmorepopularbothinChinaandabroad.LeadingChinesebike-sharingcompaniesMobikeandOfoarenowoperatinginforeigncountries,suchasSingaporeandBritain.

AndbackinChina,ifyourideyoursharedbikeandstop

tobuyabottleofwater,don'tworryifyou'veforgottenyourwallet.Youcouldeasilypaywithyoursmartphonebyscanningtheseller'sQRcode.CashlesspaymenthasgrownintoalifestylechoiceforChinesepeople—evenastreetstoresellingfruithasaQRcode.

Sowhat'snextforChina?

Itseemsthatwestillhavemanymoregreatideastolookforwardto.

26.Which

ofthefol

lowingisNOTmentionedinthepassage?

A.High-speedrailways.B.Bikesharin

g.

C.Cashlesspayment.D.Onlineshopping.

27.Wecanlearnfromthepassagethat    . 

A.theFuxingisthefastesttrainintheworld

B.Chinaistakingtheleadinhigh-speedtraintechnology

C.Chinahasbuilt60%oftheworld'stotalrailways

D.EuropehashelpedChinabuild10high-speedrailways

28.Howmanyhigh-speedtrainswerethereintheworldbytheendof2017?

A.4,500.

B.3,5

00.C.2,700.D.1,600.

29.Wh

at'sthewriter'sattitudetowardsChina'sfuturedevelopment?

A.Uncertain.B.Positive.

C.Worried.D.Critical.

Ⅳ.[2018·连云港]根据短文意思和所给首字母,写出一个完整正确的单词

T

heBambooTrain,or“Norry”inthelocallanguage,isquitefamousinCambodia.Thetrainisinfactabigbamboobedwithfourwheelsandasmallengine.Itcanrunatt

he30.s    ofupto50km/honthetracks.Lotsof31.v    gotoCambodiatoenjoytheBambooTrainride.Theyhavetopay5dollarsperpersonto32.g    onthetrain.Thebesttimetotakethetrainisfrom4to6o'clockintheafternoon,33.b    itiscoolwhenpeopleenjoythecountrysideview.“Itfeelsmorelikearollercoaster,butit'srea

llynice,”aGermanytouristTheresaKessemeiersaidaftershe34.c    aride.TheBambooTrainhasbecomeapopulartourista

ttraction. 

Ⅴ.从方框中选择恰当的词或短语并用其正确的形式填空(每个词或短语只能用一次)

asoftenaspossible;changealot;onone'sown;recent;waste

35.Asasecondarystudent,Jimcantakeabustoschool        . 

36.Thatsmallvillage     

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