新高考數(shù)學(xué)一輪復(fù)習(xí)講練測(cè)第4章第03講 三角函數(shù)的圖象與性質(zhì)（練習(xí)）（原卷版）

第03講三角函數(shù)的圖象與性質(zhì)（模擬精練+真題演練）1．（2023·陜西西安·陜西師大附中校考模擬預(yù)測(cè)）將函數(shù)SKIPIF1<0的圖像向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，得到函數(shù)SKIPIF1<0的圖像，則下列正確的是（

）A．直線SKIPIF1<0是SKIPIF1<0圖像的一條對(duì)稱軸 B．SKIPIF1<0的最小正周期為SKIPIF1<0C．SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0對(duì)稱 D．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增2．（2023·四川成都·石室中學(xué)校考模擬預(yù)測(cè)）函數(shù)SKIPIF1<0圖象的對(duì)稱軸可以是（

）A．直線SKIPIF1<0 B．直線SKIPIF1<0C．直線SKIPIF1<0 D．直線SKIPIF1<03．（2023·河南·襄城高中校聯(lián)考三模）將函數(shù)SKIPIF1<0的圖象上所有點(diǎn)向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，然后橫坐標(biāo)伸長(zhǎng)為原來(lái)的2倍，縱坐標(biāo)不變，得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0在區(qū)間SKIPIF1<0上的值域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023·重慶·統(tǒng)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，若對(duì)于任意實(shí)數(shù)x，都有SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．2 B．SKIPIF1<0 C．4 D．85．（2023·河南·校聯(lián)考模擬預(yù)測(cè)）某次實(shí)驗(yàn)得交變電流SKIPIF1<0（單位：A）隨時(shí)間SKIPIF1<0（單位：s）變化的函數(shù)解析式為SKIPIF1<0，其中SKIPIF1<0且SKIPIF1<0，其圖象如圖所示，則下列說(shuō)法錯(cuò)誤的是（

）

A．SKIPIF1<0 B．SKIPIF1<0C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0 D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<06．（2023·北京西城·北師大實(shí)驗(yàn)中學(xué)校考三模）在下列四個(gè)函數(shù)中，在定義域內(nèi)單調(diào)遞增的有（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·北京大興·校考三模）已知函數(shù)SKIPIF1<0，SKIPIF1<0，將函數(shù)SKIPIF1<0的圖象經(jīng)過(guò)下列變換可以與SKIPIF1<0的圖象重合的是（

）A．向左平移SKIPIF1<0個(gè)單位 B．向左平移SKIPIF1<0個(gè)單位C．向右平移SKIPIF1<0個(gè)單位 D．向右平移SKIPIF1<0個(gè)單位8．（2023·陜西咸陽(yáng)·武功縣普集高級(jí)中學(xué)?？寄M預(yù)測(cè)）已知函數(shù)SKIPIF1<0，則關(guān)于SKIPIF1<0的下列結(jié)論不正確的是（

）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在區(qū)間SKIPIF1<0上是單調(diào)遞減函數(shù)D．將SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位即可得到SKIPIF1<0的圖象9．（多選題）（2023·福建漳州·統(tǒng)考模擬預(yù)測(cè)）把函數(shù)SKIPIF1<0圖象上所有點(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在SKIPIF1<0上單調(diào)遞減B．SKIPIF1<0在SKIPIF1<0上有2個(gè)零點(diǎn)C．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱D．SKIPIF1<0在SKIPIF1<0上的值域?yàn)镾KIPIF1<010．（多選題）（2023·江蘇鹽城·鹽城市伍佑中學(xué)?？寄M預(yù)測(cè)）已知函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0）個(gè)單位長(zhǎng)度后對(duì)應(yīng)的函數(shù)為SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0上單調(diào)，則SKIPIF1<0的可取（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（多選題）（2023·廣東佛山·?？寄M預(yù)測(cè)）已知函數(shù)SKIPIF1<0的初相為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．函數(shù)SKIPIF1<0的一個(gè)單調(diào)遞減區(qū)間為SKIPIF1<0C．若把函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長(zhǎng)度得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0為偶函數(shù)D．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的值域?yàn)镾KIPIF1<012．（多選題）（2023·湖南衡陽(yáng)·衡陽(yáng)市八中?？寄M預(yù)測(cè)）已知函數(shù)SKIPIF1<0，其圖象相鄰對(duì)稱軸間的距離為SKIPIF1<0，點(diǎn)SKIPIF1<0是其中的一個(gè)對(duì)稱中心，則下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0B．函數(shù)SKIPIF1<0圖象的一條對(duì)稱軸方程是SKIPIF1<0C．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增D．將函數(shù)SKIPIF1<0圖象上所有點(diǎn)橫坐標(biāo)伸長(zhǎng)原來(lái)的2倍，縱坐標(biāo)縮短原來(lái)的一半，再把得到的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度，可得到正弦函數(shù)SKIPIF1<0的圖象13．（2023·河北滄州·?？寄M預(yù)測(cè)）若函數(shù)SKIPIF1<0為奇函數(shù)，則SKIPIF1<0的最小值為______.14．（2023·陜西咸陽(yáng)·武功縣普集高級(jí)中學(xué)校考模擬預(yù)測(cè)）已知SKIPIF1<0，當(dāng)SKIPIF1<0（其中SKIPIF1<0）時(shí)，SKIPIF1<0有且只有一個(gè)解，則SKIPIF1<0的取值范圍是____________.15．（2023·江蘇鎮(zhèn)江·江蘇省鎮(zhèn)江中學(xué)?？既＃懗鲆粋€(gè)同時(shí)具有下列性質(zhì)①②③，且定義域?yàn)閷?shí)數(shù)集SKIPIF1<0的函數(shù)SKIPIF1<0__________.①最小正周期為2；②SKIPIF1<0；③無(wú)零點(diǎn).16．（2023·上海徐匯·位育中學(xué)?？寄M預(yù)測(cè)）若函數(shù)SKIPIF1<0的圖像向右平移SKIPIF1<0個(gè)單位長(zhǎng)度后得到函數(shù)SKIPIF1<0的圖像，若對(duì)滿足SKIPIF1<0的SKIPIF1<0，SKIPIF1<0，有SKIPIF1<0的最小值為SKIPIF1<0，則SKIPIF1<0________．17．（2023·湖南岳陽(yáng)·統(tǒng)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0的部分圖象如圖所示.(1)求SKIPIF1<0的最小正周期及解析式；(2)將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長(zhǎng)度得到函數(shù)SKIPIF1<0的圖象，求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值和最小值.18．（2023·黑龍江哈爾濱·哈爾濱市第六中學(xué)校?？既＃┮阎瘮?shù)SKIPIF1<0，其圖象的一條對(duì)稱軸與相鄰對(duì)稱中心的橫坐標(biāo)相差SKIPIF1<0，______，從以下兩個(gè)條件中任選一個(gè)補(bǔ)充在空白橫線中.①函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度后得到的圖象關(guān)于y軸對(duì)稱且SKIPIF1<0；②函數(shù)SKIPIF1<0的圖象的一個(gè)對(duì)稱中心為SKIPIF1<0且SKIPIF1<0.(1)求函數(shù)SKIPIF1<0的解析式；(2)將函數(shù)SKIPIF1<0圖象上所有點(diǎn)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在區(qū)間SKIPIF1<0上恰有3個(gè)零點(diǎn)，求t的取值范圍.19．（2023·湖南常德·常德市一中校考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上恰有3個(gè)零點(diǎn)，其中SKIPIF1<0為正整數(shù).(1)求函數(shù)SKIPIF1<0的解析式；(2)將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位得到函數(shù)SKIPIF1<0的圖象，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間.20．（2023·黑龍江哈爾濱·哈師大附中?？寄M預(yù)測(cè)）將函數(shù)SKIPIF1<0的圖象先向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，再將所得函圖象上所有點(diǎn)的橫坐標(biāo)變?yōu)樵瓉?lái)的SKIPIF1<0（ω＞0）倍（縱坐標(biāo)不變），得到函數(shù)SKIPIF1<0的圖象．(1)若SKIPIF1<0，求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值；(2)若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上沒有零點(diǎn)，求ω的取值范圍．1．（2023?天津）已知函數(shù)SKIPIF1<0的一條對(duì)稱軸為直線SKIPIF1<0，一個(gè)周期為4，則SKIPIF1<0的解析式可能為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022?天津）已知SKIPIF1<0，關(guān)于該函數(shù)有下列四個(gè)說(shuō)法：①SKIPIF1<0的最小正周期為SKIPIF1<0；②SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上單調(diào)遞增；③當(dāng)SKIPIF1<0，SKIPIF1<0時(shí)，SKIPIF1<0的取值范圍為SKIPIF1<0，SKIPIF1<0；④SKIPIF1<0的圖象可由SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度得到．以上四個(gè)說(shuō)法中，正確的個(gè)數(shù)為SKIPIF1<0SKIPIF1<0A．1 B．2 C．3 D．43．（2022?浙江）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)SKIPIF1<0SKIPIF1<0A．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4．（2022?新高考Ⅰ）記函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0．若SKIPIF1<0，且SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0，SKIPIF1<0中心對(duì)稱，則SKIPIF1<0SKIPIF1<0A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．35．（2022?甲卷）將函數(shù)SKIPIF1<0的圖像向左平移SKIPIF1<0個(gè)單位長(zhǎng)度后得到曲線SKIPIF1<0，若SKIPIF1<0關(guān)于SKIPIF1<0軸對(duì)稱，則SKIPIF1<0的最小值是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022?甲卷）設(shè)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0恰有三個(gè)極值點(diǎn)、兩個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<07．（多選題）（2022?新高考Ⅱ）已知函數(shù)SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0，SKIPIF1<0中心對(duì)稱，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0在區(qū)間SKIPIF1<0單調(diào)遞減 B．SKIPIF1<0在區(qū)間SKIPIF1<0，SKIPIF1<0有兩個(gè)極值點(diǎn) C．直線SKIPIF1<0是曲線SKIPIF1<0的對(duì)稱軸 D．直線SKIPIF1<0是曲線SKIPIF1<0的切線8．（2023?新高考Ⅱ）已知函數(shù)SKIPIF1<0，如圖，SKIPIF1<0，SKIPIF1<0是直線SKIPI