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天一大联考 2023-2024学年高一年级阶段性测试(二)2数学.考卷答案试卷答案
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【附】听力录音稿(Text1)W:Whatwouldyouliketostart?ThesouplooksniceM:OK.I'llhavethesouptoo.Andforthemaincourse(主菜)？W:I'dlikethebutterchicken(Text2)W:CanItakethishat,please?M:Sure.That'sS27.50.Willthatbecash(现金)，check(支票)，orcreditcard(信用卡)？W:Ihavenocreditcard.Iwillpayincash.(Text3)M:Wouldyoupleasegivemeacupofgreentea,please?W:Sorry,butthereisonlycoffeeandwaterleft.M:Thengivemeaglassofwater,please.(Text4)M:So,whenaretheotherguysgoingtogethere?Thetrainisleavingin10minutes.Wecan'twaithereforever.W:It's10:30already.Theyaresupposedtobeherebynow.Itoldeverybodytomeethereby10:15.(Text5)M:Mary,mybrotherandIaregoingtowatchBattleofChosinReservoir)Wouldyouliketocometojoinus?W:Sure.EveryoneonTVistalkingaboutthemovieM:Let'smeetat6pmatmyplace.Mybrotherwilldriveusthere.(Text6)W:WhereareyouplanningtotravelinApril,Jack?M:I'mthinkingoftravelingtoBoston.W:Why?M:IwanttowatchtheBostonMarathon!It'sonApril20,soI'llbebackbeforeMayIst.W:Whynottakepartinthemarathon?M:Well,youneedalotoftrainingtotakepartinamarathon,andIhaven'tdoneanytrainingatall.PerhapsIcannextyear.(Text7)W:Haveyoufinishedpackingyet,David?M:I'vegotlotsofT-shirtsinthesuitcase,Mum,butIcan'tfindmysunglassesanywhere.W:IsawtheminyourbedroomwhenIwascleaningthehouse.Whataboutshorts?I'msureyoursarealltoosmallforyounow.M:You'reright.Let'sgetsomenewoneswhenwegoshoppingtomorrow.(Text8)W:Henry,youlooklikeyou'reontopoftheworld.What'sup?M:Ijustheardsomegoodnewsfromourheadteacher.W:Whatwasit?Hasourschoolfootballteamwonthefootballmatch?M:No,itwasn'tthat.IjustgotthenewsthatthepaintingIfinishedlastmonthhasbeenchosentobeexhibitedintheCity'sStudentArtShowW:Really?That'sgreatnews.M:Sodoyouwanttogototheshow?W:Sure.Whenwillitbeheld?M:From9amto4pmnextMonday.Ireallycan'twaittogo.湖北省孝感市重，点高中教科研协作体*英语答案（共8页）第7页
分析（1）根据函数奇偶性的定义进行判断即可．
（2）根据函数单调性的定义和性质进行证明即可．
解答解：（1）f（x）的定义域为{x|x≠0}关于原点对称，$f（x）=\frac{{a（{a^x}+1）}}{{2（{{a^x}-1}）}}$，
∴$f（-x）=\frac{{a（{a^{-x}}+1）}}{{2（{a^{-x}}-1）}}=\frac{{a（1+{a^x}）}}{{2（1-{a^x}）}}=-f（x）$，所以f（x）为奇函数．
（2）任取x1，x2∈R，且x1＜x2，则$f（{x_1}）-f（{x_2}）=\frac{{a（{a^{x_2}}-{a^{x_1}}）}}{{（{a^{x_1}}-1）（{a^{x_2}}-1）}}$，
∵a＞1，∴${a^{x_1}}＜{a^{x_2}}$，若x∈（0，+∞），${a^{x_1}}-1＞0$，${a^{x_2}}-1＞0$，
∴f（x1）＞f（x2），
∴f（x）在（-∞，0）和（0，+∞）上为减函数．
点评本题主要考查函数奇偶性和单调性的判断，利用定义法是解决本题的关键．
