新高考數(shù)學(xué)二輪復(fù)習(xí)講義專題08 三角函數(shù)圖像與性質(zhì)（原卷版）

專題09講：三角函數(shù)圖像與性質(zhì)【考點(diǎn)專題】1．正弦、余弦、正切函數(shù)的圖象與性質(zhì)(下表中k∈Z)函數(shù)y＝sinxy＝cosxy＝tanx圖象定義域RReq\b\lc\{\rc\}(\a\vs4\al\co1(x\b\lc\|\rc\(\a\vs4\al\co1(x≠kπ＋\f(π,2)))))值域[－1,1][－1,1]R周期性2π2ππ奇偶性奇函數(shù)偶函數(shù)奇函數(shù)遞增區(qū)間eq\b\lc\[\rc\](\a\vs4\al\co1(2kπ－\f(π,2)，2kπ＋\f(π,2)))[2kπ－π，2kπ]SKIPIF1<0遞減區(qū)間eq\b\lc\[\rc\](\a\vs4\al\co1(2kπ＋\f(π,2)，2kπ＋\f(3π,2)))[2kπ，2kπ＋π]對(duì)稱中心(kπ，0)eq\b\lc\(\rc\)(\a\vs4\al\co1(kπ＋\f(π,2)，0))eq\b\lc\(\rc\)(\a\vs4\al\co1(\f(kπ,2)，0))對(duì)稱軸方程x＝kπ＋eq\f(π,2)x＝kπ2．簡(jiǎn)諧運(yùn)動(dòng)的有關(guān)概念y＝Asin(ωx＋φ)(A>0，ω>0)，x≥0振幅周期頻率相位初相AT＝eq\f(2π,ω)f＝eq\f(1,T)＝eq\f(ω,2π)ωx＋φφ3．用“五點(diǎn)法”畫y＝Asin(ωx＋φ)(A>0，ω>0)一個(gè)周期內(nèi)的簡(jiǎn)圖時(shí)，要找五個(gè)特征點(diǎn)xeq\f(0－φ,ω)eq\f(\f(π,2)－φ,ω)eq\f(π－φ,ω)eq\f(\f(3π,2)－φ,ω)eq\f(2π－φ,ω)ωx＋φ0eq\f(π,2)πeq\f(3π,2)2πy＝Asin(ωx＋φ)0A0－A04．函數(shù)y＝sinx的圖象經(jīng)變換得到y(tǒng)＝Asin(ωx＋φ)(A>0，ω>0)的圖象的兩種途徑【方法技巧】1．求解三角函數(shù)的值域(最值)常見到以下幾種類型(1)形如y＝asinx＋bcosx＋c的三角函數(shù)化為y＝Asin(ωx＋φ)＋c的形式，再求值域(最值)．求三角函數(shù)取最值時(shí)相應(yīng)自變量x的集合時(shí)，要注意考慮三角函數(shù)的周期性．(2)形如y＝asin2x＋bsinx＋c(或y＝acos2x＋bcosx＋c)，x∈D的函數(shù)的值域或最值時(shí)，通過(guò)換元，令t＝sinx(或cosx)，將原函數(shù)轉(zhuǎn)化為關(guān)于t的二次函數(shù)，利用配方法求值域或最值即可．求解過(guò)程中要注意t＝sinx(或cosx)的有界性．(3)形如y＝asinxcosx＋b(sinx±cosx)＋c的三角函數(shù)，可先設(shè)t＝sinx±cosx，化為關(guān)于t的二次函數(shù)求值域(最值)．2．求三角函數(shù)周期的方法(1)定義法：即利用周期函數(shù)的定義求解．(2)公式法：對(duì)形如y＝Asin(ωx＋φ)或y＝Acos(ωx＋φ)(A，ω，φ是常數(shù)，A≠0，ω≠0)的函數(shù)，T＝eq\f(2π,|ω|)；對(duì)形如y＝Atan(ωx＋φ)(A，ω，φ是常數(shù)，A≠0，ω≠0)的函數(shù)，SKIPIF1<0．形如y＝|Asinωx|(或y＝|Acosωx|)的函數(shù)的周期T＝eq\f(π,|ω|).(3)觀察法：即通過(guò)觀察函數(shù)圖象求其周期．3．三角函數(shù)周期性與奇偶性、對(duì)稱性的解題策略(1)探求三角函數(shù)的周期，常用方法是公式法，即將函數(shù)化為y＝Asin(ωx＋φ)或y＝Acos(ωx＋φ)的形式，再利用公式求解．(2)判斷函數(shù)y＝Asin(ωx＋φ)或y＝Acos(ωx＋φ)是否具備奇偶性，關(guān)鍵是看它能否通過(guò)誘導(dǎo)公式轉(zhuǎn)化為y＝Asinωx(Aω≠0)或y＝Acosωx(Aω≠0)其中的一個(gè)．(3)對(duì)于可化為f(x)＝Asin(ωx＋φ)(或f(x)＝Acos(ωx＋φ))形式的函數(shù)，如果求f(x)的對(duì)稱軸，只需令ωx＋φ＝eq\f(π,2)＋kπ(k∈Z)(或令ωx＋φ＝kπ(k∈Z))，求x即可；如果求f(x)的對(duì)稱中心的橫坐標(biāo)，只需令ωx＋φ＝kπ(k∈Z)(或令ωx＋φ＝eq\f(π,2)＋kπ(k∈Z))，求x即可．(4)對(duì)于可化為f(x)＝Atan(ωx＋φ)形式的函數(shù)，如果求f(x)的對(duì)稱中心的橫坐標(biāo)，只需令ωx＋φ＝eq\f(kπ,2)(k∈Z)，求x即可．4．求函數(shù)y＝tan(ωx＋φ)的單調(diào)區(qū)間的方法y＝tan(ωx＋φ)(ω>0)的單調(diào)區(qū)間的求法是把ωx＋φ看成一個(gè)整體，解－eq\f(π,2)＋kπ<ωx＋φ<eq\f(π,2)＋kπ，k∈Z即可．當(dāng)ω<0時(shí)，先用誘導(dǎo)公式把ω化為正值再求單調(diào)區(qū)間．5．(1)由函數(shù)y＝sinx的圖象通過(guò)變換得到y(tǒng)＝Asin(ωx＋φ)的圖象有兩條途徑：“先平移后伸縮”與“先伸縮后平移”．(2)當(dāng)x的系數(shù)不為1時(shí)，特別注意先提取系數(shù)，再加減．(3)橫向伸縮變換，只變?chǔ)兀詹话l(fā)生變化.6．若設(shè)所求解析式為y＝Asin(ωx＋φ)，則在觀察函數(shù)圖象的基礎(chǔ)上，可按以下規(guī)律來(lái)確定A，ω，φ.(1)由函數(shù)圖象上的最大值、最小值來(lái)確定|A|.(2)由函數(shù)圖象與x軸的交點(diǎn)確定T，由T＝eq\f(2π,ω)，確定ω.(3)y＝Asin(ωx＋φ)中φ的確定方法①代入法：把圖象上的一個(gè)已知點(diǎn)代入(此時(shí)A，ω已知)或代入圖象與x軸的交點(diǎn)求解(此時(shí)要注意交點(diǎn)在上升區(qū)間上還是在下降區(qū)間上)，或把圖象的最高點(diǎn)或最低點(diǎn)代入．②五點(diǎn)對(duì)應(yīng)法：確定φ值時(shí)，往往以尋找“五點(diǎn)法”中的特殊點(diǎn)作為突破口.“五點(diǎn)”的ωx＋φ的值具體如下：“第一點(diǎn)”(即圖象上升時(shí)與x軸的交點(diǎn))為ωx＋φ＝0；“第二點(diǎn)”(即圖象的“峰點(diǎn)”)為ωx＋φ＝eq\f(π,2)；“第三點(diǎn)”(即圖象下降時(shí)與x軸的交點(diǎn))為ωx＋φ＝π；“第四點(diǎn)”(即圖象的“谷點(diǎn)”)為ωx＋φ＝eq\f(3π,2)；“第五點(diǎn)”為ωx＋φ＝2π.【核心題型】題型一：整體代入法求三角函數(shù)的單調(diào)區(qū)間、對(duì)稱軸和對(duì)稱中心1．（2023春·河北·高二統(tǒng)考學(xué)業(yè)考試）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022秋·安徽·高三校聯(lián)考開學(xué)考試）函數(shù)SKIPIF1<0的圖象的一個(gè)對(duì)稱中心為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022秋·廣西欽州·高三校考階段練習(xí)）已知函數(shù)SKIPIF1<0且SKIPIF1<0，則函數(shù)SKIPIF1<0的圖象的一條對(duì)稱軸是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型二：代入檢驗(yàn)法判斷三角函數(shù)的單調(diào)區(qū)間、對(duì)稱軸和對(duì)稱中心4．（2023春·河南·高三商丘市回民中學(xué)校聯(lián)考開學(xué)考試）將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度，得到函數(shù)SKIPIF1<0的圖象，下列說(shuō)法正確的是（

）．A．SKIPIF1<0為奇函數(shù) B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減C．SKIPIF1<0在SKIPIF1<0上的值域?yàn)镾KIPIF1<0 D．點(diǎn)SKIPIF1<0是SKIPIF1<0圖象的一個(gè)對(duì)稱中心5．（2022秋·天津河西·高三天津市海河中學(xué)?？计谀┮阎瘮?shù)SKIPIF1<0，給出以下四個(gè)命題：①SKIPIF1<0的最小正周期為SKIPIF1<0；②SKIPIF1<0在SKIPIF1<0上的值域?yàn)镾KIPIF1<0；③SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0中心對(duì)稱；④SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對(duì)稱．其中正確命題的個(gè)數(shù)是（

）A．1 B．2 C．3 D．46．（多選）（2022秋·山西晉中·高三校聯(lián)考階段練習(xí)）關(guān)于函數(shù)SKIPIF1<0，下列說(shuō)法正確的是（

）A．函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減B．函數(shù)SKIPIF1<0的圖像關(guān)于SKIPIF1<0中心對(duì)稱C．函數(shù)SKIPIF1<0的對(duì)稱軸方程為SKIPIF1<0，SKIPIF1<0D．將SKIPIF1<0的圖像向右平移SKIPIF1<0個(gè)單位長(zhǎng)度后，可以得到SKIPIF1<0的圖像題型三：圖像法求三角函數(shù)最值或值域7．（2021春·上海普陀·高一曹楊二中?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0，則SKIPIF1<0的最小值是_________.8．（2022秋·北京·高三北京市八一中學(xué)?？茧A段練習(xí)）定義運(yùn)算SKIPIF1<0例如，SKIPIF1<0，則函數(shù)SKIPIF1<0的值域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，求SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值和最小值.題型四：換元法求三角函數(shù)最值或值域10．（2023·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的最大值為（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．311．（2022·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的值域?yàn)開_______．12．（2022·全國(guó)·高三專題練習(xí)）函數(shù)y＝cos2x－sinx的值域是__________________題型五：利用三角函數(shù)單調(diào)性、奇偶性、周期性和對(duì)稱性求參數(shù)的值13．（2023秋·廣西南寧·高三南寧二中?？计谀┮阎瘮?shù)SKIPIF1<0的兩個(gè)相鄰的對(duì)稱中心的間距為SKIPIF1<0，現(xiàn)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位后得到一個(gè)奇函數(shù)，則SKIPIF1<0的一個(gè)可能取值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．0 D．SKIPIF1<014．（2023·全國(guó)·校聯(lián)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．（多選）（2023秋·黑龍江哈爾濱·高三哈爾濱市第六中學(xué)校校考期末）已知函數(shù)SKIPIF1<0SKIPIF1<0的最小正周期為SKIPIF1<0，函數(shù)SKIPIF1<0圖象關(guān)于直線SKIPIF1<0對(duì)稱，且滿足函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型六：五點(diǎn)法求三角函數(shù)解析式16．（2020·全國(guó)·統(tǒng)考高考真題）設(shè)函數(shù)SKIPIF1<0在SKIPIF1<0的圖像大致如下圖，則f(x)的最小正周期為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<017．（2022·山西運(yùn)城·校聯(lián)考模擬預(yù)測(cè)）設(shè)函數(shù)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）的部分圖象如圖所示.若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<018．（多選）（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的部分圖象如圖所示，則（

）A．SKIPIF1<0的最小正周期為SKIPIF1<0B．SKIPIF1<0為偶函數(shù)C．SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)的最小值為1D．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱題型七：三角函數(shù)圖像的伸縮變換問(wèn)題19．（2023·全國(guó)·高三專題練習(xí)）為了得到函數(shù)SKIPIF1<0的圖象，只要把函數(shù)SKIPIF1<0圖象上所有的點(diǎn)（

）A．向左平移SKIPIF1<0個(gè)單位長(zhǎng)度 B．向右平移SKIPIF1<0個(gè)單位長(zhǎng)度C．向左平移SKIPIF1<0個(gè)單位長(zhǎng)度 D．向右平移SKIPIF1<0個(gè)單位長(zhǎng)度20．（2021·全國(guó)·統(tǒng)考高考真題）把函數(shù)SKIPIF1<0圖像上所有點(diǎn)的橫坐標(biāo)縮短到原來(lái)的SKIPIF1<0倍，縱坐標(biāo)不變，再把所得曲線向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，得到函數(shù)SKIPIF1<0的圖像，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<021．（2022·全國(guó)·高三專題練習(xí)）若函數(shù)SKIPIF1<0在SKIPIF1<0處有最小值，為了得到SKIPIF1<0的圖象，則只要將SKIPIF1<0的圖象（

）A．向右平移SKIPIF1<0個(gè)單位長(zhǎng)度 B．向左平移SKIPIF1<0個(gè)單位長(zhǎng)度C．向左平移SKIPIF1<0個(gè)單位長(zhǎng)度 D．向右平移SKIPIF1<0個(gè)單位長(zhǎng)度【高考必刷】一、單選題1．（2023春·安徽安慶·高一安徽省宿松中學(xué)?？奸_學(xué)考試）設(shè)函數(shù)SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱B．SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱C．SKIPIF1<0是偶函數(shù)D．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增2．（2022·高一課時(shí)練習(xí)）函數(shù)SKIPIF1<0的單調(diào)增區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2021秋·云南昆明·高三昆明市第三中學(xué)?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0的圖像關(guān)于SKIPIF1<0對(duì)稱，則函數(shù)SKIPIF1<0的圖像的一條對(duì)稱軸是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022秋·河南鄭州·高三統(tǒng)考期末）若將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度，再將圖象上所有點(diǎn)的橫坐標(biāo)縮短到原來(lái)的SKIPIF1<0，得到函數(shù)SKIPIF1<0的圖象，則函數(shù)SKIPIF1<0圖象的對(duì)稱軸可能是（

）A．直線SKIPIF1<0 B．直線SKIPIF1<0C．直線SKIPIF1<0 D．直線SKIPIF1<05．（2022秋·河南洛陽(yáng)·高三校聯(lián)考階段練習(xí)）函數(shù)SKIPIF1<0的最大值為2，且對(duì)任意的SKIPIF1<0，SKIPIF1<0恒成立，SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的值為（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．26．（2023秋·江蘇泰州·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的最小正周期SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·甘肅·模擬預(yù)測(cè)）設(shè)函數(shù)SKIPIF1<0的部分圖象如圖所示，若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022秋·江蘇南通·高三?？计谥校┖瘮?shù)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0，SKIPIF1<0）的部分圖象如圖所示，將SKIPIF1<0的圖象上所有點(diǎn)的橫坐標(biāo)擴(kuò)大到原來(lái)的4倍（縱坐標(biāo)不變），再把所得的圖象沿SKIPIF1<0軸向左平移SKIPIF1<0個(gè)單位長(zhǎng)度，得到函數(shù)SKIPIF1<0的圖象，則函數(shù)SKIPIF1<0的一個(gè)單調(diào)遞增區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2020秋·北京·高三北京八中校考期中）已知SKIPIF1<0,SKIPIF1<0，直線SKIPIF1<0＝SKIPIF1<0和SKIPIF1<0＝SKIPIF1<0是函數(shù)SKIPIF1<0圖象的兩條相鄰的對(duì)稱軸，則SKIPIF1<0＝（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2022·四川內(nèi)江·四川省內(nèi)江市第六中學(xué)校考模擬預(yù)測(cè)）設(shè)函數(shù)SKIPIF1<0，其中SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0在SKIPIF1<0上的單調(diào)減區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（2022·全國(guó)·高三專題練習(xí)）如圖，點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0分別是函數(shù)SKIPIF1<0(SKIPIF1<0，SKIPIF1<0，SKIPIF1<0)圖像上的最低點(diǎn)和最高點(diǎn)，若SKIPIF1<0、SKIPIF1<0兩點(diǎn)間的距離為SKIPIF1<0，則關(guān)于函數(shù)SKIPIF1<0的說(shuō)法正確的是（

）A．在區(qū)間SKIPIF1<0上單調(diào)遞增 B．在區(qū)間SKIPIF1<0上單調(diào)遞減C．在區(qū)間SKIPIF1<0上單調(diào)遞減 D．在區(qū)間SKIPIF1<0上單調(diào)遞增12．（2022秋·湖南懷化·高三?？奸_學(xué)考試）已知函數(shù)SKIPIF1<0的部分圖象如圖所示，點(diǎn)SKIPIF1<0，SKIPIF1<0，則下列說(shuō)法中錯(cuò)誤的是（）A．直線SKIPIF1<0是圖象的一條對(duì)稱軸B．SKIPIF1<0的圖象可由SKIPIF1<0向左平移SKIPIF1<0個(gè)單位而得到C．的最小正周期為SKIPIF1<0D．在區(qū)間SKIPIF1<0上單調(diào)遞增13．（2021春·廣東東莞·高三東莞市光明中學(xué)校考開學(xué)考試）函數(shù)SKIPIF1<0的圖象如圖所示，為了得到SKIPIF1<0的圖象，只需將SKIPIF1<0的圖象（

）A．向右平移SKIPIF1<0個(gè)單位長(zhǎng)度B．向左平移SKIPIF1<0個(gè)單位長(zhǎng)度C．向右平移SKIPIF1<0個(gè)單位長(zhǎng)度D．向左平移SKIPIF1<0個(gè)單位長(zhǎng)度14．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，其部分圖象如圖所示，則下列關(guān)于SKIPIF1<0的結(jié)論錯(cuò)誤的是（

）．A．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增B．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱C．SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱D．SKIPIF1<0的圖象可由函數(shù)SKIPIF1<0圖象上所有點(diǎn)的縱坐標(biāo)不變，橫坐標(biāo)變?yōu)樵瓉?lái)的SKIPIF1<0倍得到15．（2022·全國(guó)·高三專題練習(xí)）將函數(shù)SKIPIF1<0的圖象先向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，再把所得函數(shù)圖象的橫坐標(biāo)變?yōu)樵瓉?lái)的SKIPIF1<0倍，縱坐標(biāo)不變，得到函數(shù)SKIPIF1<0的圖象，若函數(shù)SKIPIF1<0在SKIPIF1<0上沒有零點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<016．（2022秋·河南·高三校聯(lián)考階段練習(xí)）若將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長(zhǎng)度后為奇函數(shù)，則SKIPIF1<0的值可以為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<017．（2022·全國(guó)·高三專題練習(xí)）已知把函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，再把橫坐標(biāo)縮小到原來(lái)一半，縱坐標(biāo)不變，得到函數(shù)SKIPIF1<0的圖象，若SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<018．（2021·全國(guó)·高三專題練習(xí)）把函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位后，得到函數(shù)SKIPIF1<0的圖象，若函數(shù)SKIPIF1<0是偶函數(shù)，則下列數(shù)中可能是SKIPIF1<0的值的為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<019．（2022春·河南鄭州·高三校聯(lián)考階段練習(xí)）將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0SKIPIF1<0個(gè)單位長(zhǎng)度，再將圖象上各點(diǎn)的橫坐標(biāo)伸長(zhǎng)到原來(lái)的SKIPIF1<0倍（縱坐標(biāo)不變），得到函數(shù)SKIPIF1<0的圖象，若對(duì)任意的SKIPIF1<0均有SKIPIF1<0成立，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<020．（2022秋·河南·高三安陽(yáng)一中校聯(lián)考階段練習(xí)）函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）在一個(gè)周期內(nèi)的圖象如圖所示，將函數(shù)SKIPIF1<0圖象上的點(diǎn)的橫坐標(biāo)伸長(zhǎng)為原來(lái)的2倍，再向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．－1 D．SKIPIF1<021．（2023·高三課時(shí)練習(xí)）已知函數(shù)SKIPIF1<0（SKIPIF1<0）在區(qū)間SKIPIF1<0上有且僅有一個(gè)最大值和一個(gè)最小值，則實(shí)數(shù)SKIPIF1<0的取值不可能是（

）A．SKIPIF1<0 B．3 C．SKIPIF1<0 D．4二、多選題22．（2021·高一單元測(cè)試）已知函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則下列說(shuō)法正確的有（

）A．SKIPIF1<0B．SKIPIF1<0C．直線SKIPIF1<0是SKIPIF1<0圖象的一條對(duì)稱軸D．點(diǎn)SKIPIF1<0是SKIPIF1<0圖象的一個(gè)對(duì)稱中心23．（2022秋·遼寧大連·高三統(tǒng)考期末）將函數(shù)SKIPIF1<0圖象上所有的點(diǎn)向左平移SKIPIF1<0個(gè)單位長(zhǎng)度，得到函數(shù)SKIPIF1<0的圖象，則（

）A．SKIPIF1<0的最小正周期為SKIPIF1<0B．SKIPIF1<0圖象的一個(gè)對(duì)稱中心為SKIPIF1<0C．SKIPIF1<0的單調(diào)遞減區(qū)間為SKIPIF1<0D．SKIPIF1<0的圖象與函數(shù)SKIPIF1<0的圖象重合24．（2023秋·河北唐山·高一灤南縣第一中學(xué)?？计谀┰O(shè)函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0為偶函數(shù)，則SKIPIF1<0的值可以是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2023春·全國(guó)·高三校聯(lián)考開學(xué)考試）記函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0，且SKIPIF1<0，函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．當(dāng)SKIPIF1<0取得最小值時(shí)，SKIPIF1<026．（2023春·河北邯鄲·高三校聯(lián)考開學(xué)考試）若函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0，則（

）A．SKIPIF1<0B．SKIPIF1<0的圖象與函數(shù)SKIPIF1<0的圖象重合C．SKIPIF1<0D．存在唯一的SKIPIF1<0，使得SKIPIF1<027．（2022秋·河北唐山·高三?？奸_學(xué)考試）已知函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0，將SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度，再把得到的曲線上各點(diǎn)的橫坐標(biāo)伸長(zhǎng)到原來(lái)的2倍（縱坐標(biāo)不變），得到函數(shù)SKIPIF1<0的圖象，則下列結(jié)論正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0在SKIPIF1<0單調(diào)遞增C．SKIPIF1<0的圖象關(guān)于SKIPIF1<0對(duì)稱 D．SKIPIF1<0在SKIPIF1<0上的最大值是1三、填空題28．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的圖象如圖所示，則函數(shù)SKIPIF1<0的最大值為________．29．（2021·浙江·高三專題練習(xí)）已知函數(shù)SKIPIF1<0圖象的一條對(duì)稱軸為SKIPIF1<0，則SKIPIF1<0___________，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的值域?yàn)開__________．30．（2023秋·山東東營(yíng)·高三東營(yíng)市第一中學(xué)?？计谀┮阎瘮?shù)SKIPIF1<0，SKIPIF1<0為其圖象的對(duì)稱中心，B、C是該圖象上相鄰的最高點(diǎn)和最低點(diǎn)．若SKIPIF1<0，則SKIPIF1<0的解析式為________．31．（2023春·安徽·高三合肥市第八中學(xué)校聯(lián)考開學(xué)考試）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0_________．32．（2022秋·山東東營(yíng)·高三勝利一中?？计谀┰O(shè)函數(shù)SKIPIF1<0，直線SKIPIF1<0為SKIPIF1<0圖像的對(duì)稱軸，SKIPIF1<0為SKIPIF1<0的零點(diǎn)，且SKIPIF1<0的最小正周期大于SKIPIF1<0，則SKIPIF1<0________