高考數(shù)學(xué)二輪復(fù)習(xí)核心專題講練：三角函數(shù)與解三角形第1講 三角函數(shù)的圖象與性質(zhì) 原卷版

第1講三角函數(shù)的圖象與性質(zhì)目錄第一部分：知識(shí)強(qiáng)化第二部分：重難點(diǎn)題型突破突破一：三角函數(shù)的周期性突破二：三角函數(shù)的奇偶性突破三：三角函數(shù)的對(duì)稱性突破四：三角函數(shù)圖象變換突破五：根據(jù)圖象求解析式突破六：五點(diǎn)法作圖問題突破七：和三角函數(shù)有關(guān)的零點(diǎn)問題

第三部分：沖刺重難點(diǎn)特訓(xùn)第一部分：知識(shí)強(qiáng)化1、三角函數(shù)的周期性函數(shù)SKIPIF1<0SKIPIF1<0SKIPIF1<0周期SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0函數(shù)SKIPIF1<0SKIPIF1<0SKIPIF1<0周期SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0函數(shù)SKIPIF1<0(SKIPIF1<0)SKIPIF1<0(SKIPIF1<0)SKIPIF1<0(SKIPIF1<0)周期SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<02、三角函數(shù)的奇偶性三角函數(shù)SKIPIF1<0取何值為奇函數(shù)SKIPIF1<0取何值為偶函數(shù)SKIPIF1<0SKIPIF1<0(SKIPIF1<0)SKIPIF1<0(SKIPIF1<0)SKIPIF1<0SKIPIF1<0(SKIPIF1<0)SKIPIF1<0(SKIPIF1<0)SKIPIF1<0SKIPIF1<0(SKIPIF1<0)3、三角函數(shù)的對(duì)稱性(1)函數(shù)SKIPIF1<0的圖象的對(duì)稱軸由SKIPIF1<0(SKIPIF1<0)解得，對(duì)稱中心的橫坐標(biāo)由SKIPIF1<0(SKIPIF1<0)解得；(2)函數(shù)SKIPIF1<0的圖象的對(duì)稱軸由SKIPIF1<0(SKIPIF1<0)解得，對(duì)稱中心的橫坐標(biāo)由SKIPIF1<0(SKIPIF1<0)解得；(3)函數(shù)SKIPIF1<0的圖象的對(duì)稱中心由SKIPIF1<0SKIPIF1<0)解得．4、由SKIPIF1<0的圖象變換得到SKIPIF1<0(SKIPIF1<0，SKIPIF1<0)的圖象的兩種方法(1)先平移后伸縮(2)先伸縮后平移5、根據(jù)圖象求SKIPIF1<0的解析式求SKIPIF1<0解析式SKIPIF1<0求法方法一：代數(shù)法SKIPIF1<0方法二：讀圖法SKIPIF1<0表示平衡位置；SKIPIF1<0表示振幅SKIPIF1<0求法方法一：圖中讀出周期SKIPIF1<0，利用SKIPIF1<0求解；方法二：若無法讀出周期，使用特殊點(diǎn)代入解析式但需注意根據(jù)具體題意取舍答案.SKIPIF1<0求法方法一：將最高（低）點(diǎn)代入SKIPIF1<0求解；方法二：若無最高（低）點(diǎn)，可使用其他特殊點(diǎn)代入SKIPIF1<0求解；但需注意根據(jù)具體題意取舍答案.6、五點(diǎn)法作圖SKIPIF1<0五點(diǎn)法步驟③SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0①SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0②SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0對(duì)于復(fù)合函數(shù)SKIPIF1<0，第一步：將SKIPIF1<0看做一個(gè)整體，用五點(diǎn)法作圖列表時(shí)，分別令SKIPIF1<0等于SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，對(duì)應(yīng)的SKIPIF1<0則取SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0。，（如上表中，先列出序號(hào)①②兩行）第二步：逆向解出SKIPIF1<0（如上表中，序號(hào)③行。）第三步：得到五個(gè)關(guān)鍵點(diǎn)為：SKIPIF1<0，SKIPIF1<0,SKIPIF1<0,SKIPIF1<0,SKIPIF1<0第二部分：重難點(diǎn)題型突破突破一：三角函數(shù)的周期性1．（2022·廣西桂林·模擬預(yù)測(cè)（文））函數(shù)SKIPIF1<0的最小正周期是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·陜西咸陽·二模（理））下列四個(gè)函數(shù)，以SKIPIF1<0為最小正周期，且在區(qū)間SKIPIF1<0上單調(diào)遞減的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·遼寧沈陽·三模）函數(shù)SKIPIF1<0的最小正周期為________．4．（2022·上海·模擬預(yù)測(cè)）函數(shù)SKIPIF1<0的周期為___________；5．（多選）（2022·北京東城·三模）下列函數(shù)中最小正周期不是SKIPIF1<0的周期函數(shù)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0突破二：三角函數(shù)的奇偶性1．（2022·廣西·模擬預(yù)測(cè)（理））若將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位后，所得圖象對(duì)應(yīng)的函數(shù)為奇函數(shù)，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·四川德陽·三模（理））將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度后，所得到的圖象對(duì)應(yīng)函數(shù)為奇函數(shù)，則m的最小值是___________.3．（2022·山東聊城·一模）若SKIPIF1<0為奇函數(shù)，則SKIPIF1<0___________.（填寫符合要求的一個(gè)值）4．（2022·四川瀘州·三模（文））下列函數(shù)中，定義域?yàn)镽且周期為π的偶函數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·北京·北師大實(shí)驗(yàn)中學(xué)模擬預(yù)測(cè)）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．若函數(shù)SKIPIF1<0的圖象關(guān)于原點(diǎn)對(duì)稱，則SKIPIF1<0的一個(gè)取值為_________．突破三：三角函數(shù)的對(duì)稱性1．（2022·江西南昌·高三階段練習(xí)（文））已知函數(shù)SKIPIF1<0的最小值為2，且SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·寧夏·平羅中學(xué)高三期中（文））將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度后得到曲線C，若C關(guān)于原點(diǎn)O對(duì)稱，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·陜西·武功縣教育局教育教學(xué)研究室一模（文））已知定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的一個(gè)解析式為SKIPIF1<0___________．4．（2022·江西贛州·高三期中（文））已知函數(shù)SKIPIF1<0圖象的一條對(duì)稱軸為SKIPIF1<0．若SKIPIF1<0,則SKIPIF1<0的最大______．5．（2022·內(nèi)蒙古·?？狄恢懈呷A段練習(xí)（理））函數(shù)SKIPIF1<0的圖象的對(duì)稱中心為_________突破四：三角函數(shù)圖象變換1．（2022·貴州·貴陽一中高三階段練習(xí)（文））已知函數(shù)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）的相鄰兩條對(duì)稱軸之間的距離為SKIPIF1<0，且為奇函數(shù)，將SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位得到函數(shù)SKIPIF1<0的圖象，則函數(shù)SKIPIF1<0的圖象（

）A．關(guān)于點(diǎn)SKIPIF1<0對(duì)稱 B．關(guān)于點(diǎn)SKIPIF1<0對(duì)稱C．關(guān)于直線SKIPIF1<0對(duì)稱 D．關(guān)于直線SKIPIF1<0對(duì)稱2．（多選）（2022·湖南·寧鄉(xiāng)一中高三期中）已知SKIPIF1<0是偶函數(shù)，將函數(shù)SKIPIF1<0圖像上所有點(diǎn)向右平移SKIPIF1<0個(gè)單位得到函數(shù)SKIPIF1<0的圖像，則（

）A．SKIPIF1<0在SKIPIF1<0的值域?yàn)镾KIPIF1<0 B．SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對(duì)稱C．SKIPIF1<0在SKIPIF1<0有5個(gè)零點(diǎn) D．SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0對(duì)稱3．（2022·天津·南開中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0將其圖象向左平移SKIPIF1<0個(gè)單位得到函數(shù)SKIPIF1<0圖象且函數(shù)SKIPIF1<0為偶函數(shù)，若SKIPIF1<0是使變換成立的最小正數(shù)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·湖南·高三階段練習(xí)）將函數(shù)SKIPIF1<0的圖像先向右平移SKIPIF1<0個(gè)單位，再將所得的圖像上每個(gè)點(diǎn)的橫坐標(biāo)變?yōu)樵瓉淼腟KIPIF1<0倍，得到函數(shù)SKIPIF1<0的圖像，則SKIPIF1<0的一個(gè)可能取值是______.5．（2022·重慶市云陽縣高陽中學(xué)高三階段練習(xí)（理））若SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長(zhǎng)度得到SKIPIF1<0的圖象，則SKIPIF1<0的值可以是______．（寫出滿足條件的一個(gè)值即可）突破五：根據(jù)圖象求解析式1．（2022·四川省綿陽南山中學(xué)模擬預(yù)測(cè)（理））函數(shù)SKIPIF1<0的部分圖象如圖所示，若將SKIPIF1<0圖象上的所有點(diǎn)向右平移SKIPIF1<0個(gè)單位得到函數(shù)SKIPIF1<0的圖象，則關(guān)于函數(shù)SKIPIF1<0有下列四個(gè)說法，其中正確的是（

）A．函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0B．函數(shù)SKIPIF1<0的一條對(duì)稱軸為直線SKIPIF1<0C．函數(shù)SKIPIF1<0的一個(gè)對(duì)稱中心坐標(biāo)為SKIPIF1<0D．SKIPIF1<0再向左平移SKIPIF1<0個(gè)單位得到的函數(shù)為偶函數(shù)2．（2022·四川廣安·模擬預(yù)測(cè)（文））已知函數(shù)SKIPIF1<0的部分圖象如圖所示，則下列結(jié)論正確的是（

）A．SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱B．SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位后得到SKIPIF1<0的圖象C．SKIPIF1<0在區(qū)間SKIPIF1<0的最小值為SKIPIF1<0D．SKIPIF1<0為偶函數(shù)3．（2022·貴州·貴陽一中模擬預(yù)測(cè)（文））如圖是函數(shù)SKIPIF1<0的圖像的一部分，則要得到該函數(shù)的圖像，只需要將函數(shù)SKIPIF1<0的圖像（

）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4．（2022·山東濰坊·模擬預(yù)測(cè)）函數(shù)SKIPIF1<0的部分圖像如圖所示，現(xiàn)將SKIPIF1<0的圖像向左平移SKIPIF1<0個(gè)單位長(zhǎng)度，得到函數(shù)SKIPIF1<0的圖像，則SKIPIF1<0的表達(dá)式可以為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（多選）（2022·全國(guó)·模擬預(yù)測(cè)）函數(shù)SKIPIF1<0的部分圖像如圖所示，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增 D．函數(shù)SKIPIF1<0圖像的對(duì)稱軸方程為SKIPIF1<06．（多選）（2022·江蘇徐州·模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0的部分圖象如圖所示，則關(guān)于函數(shù)SKIPIF1<0，下列結(jié)論中正確的是（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱B．函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱C．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的減區(qū)間為SKIPIF1<0D．函數(shù)SKIPIF1<0的圖象可由函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度而得到突破六：五點(diǎn)法作圖問題1．（2022·全國(guó)·高一單元測(cè)試）已知函數(shù)SKIPIF1<0．(1)用“五點(diǎn)法”在給定的坐標(biāo)系中，畫出函數(shù)SKIPIF1<0在SKIPIF1<0上的大致圖像，并寫出SKIPIF1<0圖像的對(duì)稱中心；(2)先將函數(shù)SKIPIF1<0的圖像向右平移SKIPIF1<0個(gè)單位長(zhǎng)度后，再將得到的圖像上各點(diǎn)的橫坐標(biāo)伸長(zhǎng)為原來的SKIPIF1<0倍，縱坐標(biāo)不變，得到函數(shù)SKIPIF1<0的圖像，求SKIPIF1<0在SKIPIF1<0上的值域．2．（2022·河北·滄縣中學(xué)高一階段練習(xí)）已知向量SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．(1)求函數(shù)f（x）的對(duì)稱中心；(2)利用“五點(diǎn)法”畫出函數(shù)f（x）在一個(gè)周期內(nèi)的圖象．3．（2022·陜西·西北大學(xué)附中高一階段練習(xí)）設(shè)函數(shù)f(x)＝sin（2x+φ）（﹣π＜φ＜0），y＝f(x)圖象的一條對(duì)稱軸是直線x＝SKIPIF1<0，此對(duì)稱軸相鄰的對(duì)稱中心為（SKIPIF1<0）(1)求函數(shù)y＝f(x)的解析式；(2)用五點(diǎn)法畫出函數(shù)y＝f(x)在區(qū)間[0，π]上的圖象．4．（2022·廣東·華南師范大學(xué)第二附屬中學(xué)高一期中）已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)在用“五點(diǎn)法”作函數(shù)SKIPIF1<0的圖象時(shí)，列表如下：SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<00200完成上述表格，并在坐標(biāo)系中畫出函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的圖象；(2)求函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間；(3)求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的值域.突破七：和三角函數(shù)有關(guān)的零點(diǎn)問題

1．（2022·湖北·鄖陽中學(xué)高一階段練習(xí)）已知函數(shù)SKIPIF1<0的最小正周期SKIPIF1<0．(1)求函數(shù)SKIPIF1<0單調(diào)遞增區(qū)間；(2)若函數(shù)SKIPIF1<0在SKIPIF1<0上有零點(diǎn)，求實(shí)數(shù)SKIPIF1<0的取值范圍．2．（2022·陜西·寶雞中學(xué)高三階段練習(xí)（理））已知向量SKIPIF1<0，函數(shù)SKIPIF1<0(1)求函數(shù)SKIPIF1<0的單調(diào)增區(qū)間；(2)若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有且僅有兩個(gè)零點(diǎn)，求實(shí)數(shù)k的取值范圍．3．（2022·吉林·東北師大附中模擬預(yù)測(cè)）已知SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的值域；(2)若方程SKIPIF1<0在SKIPIF1<0上的所有實(shí)根按從小到大的順序分別記為SKIPIF1<0，求SKIPIF1<0的值．第三部分：沖刺重難點(diǎn)特訓(xùn)一、單選題1．（2022·陜西·渭南市瑞泉中學(xué)高三階段練習(xí)（理））函數(shù)SKIPIF1<0零點(diǎn)的個(gè)數(shù)為（

）A．2 B．3 C．4 D．52．（2022·江西贛州·高三期中（理））函數(shù)SKIPIF1<0的部分圖象大致為（

）A． B．C． D．3．（2022·全國(guó)·高三階段練習(xí)（理））記函數(shù)SKIPIF1<0的最小正周期為T．若SKIPIF1<0，且SKIPIF1<0的圖象在點(diǎn)SKIPIF1<0處取得最大值，則SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·吉林·東北師大附中模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，現(xiàn)將SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位，再將所得圖象上各點(diǎn)的橫坐標(biāo)縮短為原來的SKIPIF1<0倍，縱坐標(biāo)不變，得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0在SKIPIF1<0的值域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·重慶南開中學(xué)高三階段練習(xí)）已知A，B是函數(shù)SKIPIF1<0的圖像上的兩個(gè)相鄰最高點(diǎn)和最低點(diǎn)，且SKIPIF1<0，為得到SKIPIF1<0的圖像，只需要將函數(shù)SKIPIF1<0的圖像（

）A．向左平移SKIPIF1<0個(gè)單位長(zhǎng)度 B．向右平移π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3個(gè)單位長(zhǎng)度6．（2022·江蘇·沭陽縣建陵高級(jí)中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0（SKIPIF1<0SKIPIF1<0，SKIPIF1<0）

的部分圖像如圖所示，則下列說法正確的是（

）A．SKIPIF1<0B．SKIPIF1<0圖像的對(duì)稱中心為SKIPIF1<0，SKIPIF1<0C．直線SKIPIF1<0是SKIPIF1<0圖像的一條對(duì)稱軸D．將SKIPIF1<0的圖像向左平移SKIPIF1<0個(gè)單位長(zhǎng)度后，可得到一個(gè)偶函數(shù)的圖像7．（2022·寧夏·銀川一中高三階段練習(xí)（理））函數(shù)SKIPIF1<0的部分圖象如圖所示，下列說法不正確的是（

）A．函數(shù)SKIPIF1<0的解析式為SKIPIF1<0B．函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為SKIPIF1<0C．為了得到函數(shù)SKIPIF1<0的圖象，只需將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，再向上平移一個(gè)單位長(zhǎng)度D．函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱8．（2022·福建龍巖·高三期中）阻尼器是一種以提供運(yùn)動(dòng)的阻力，從而達(dá)到減振效果的專業(yè)工程裝置．深圳一高樓平安金融中心的阻尼器減震裝置，是亞洲最大的阻尼器，被稱為“鎮(zhèn)樓神器”，由物理學(xué)知識(shí)可知，某阻尼器模型的運(yùn)動(dòng)過程可近似為單擺運(yùn)動(dòng)，其離開平衡位置的位移s（單位；cm）和時(shí)間t（單位：s）的函數(shù)關(guān)系式為SKIPIF1<0，若振幅是2，圖像上相鄰最高點(diǎn)和最低點(diǎn)的距離是5，且過點(diǎn)SKIPIF1<0，則SKIPIF1<0和SKIPIF1<0的值分別為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．（2022·吉林·東北師大附中模擬預(yù)測(cè)）設(shè)函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0，且過點(diǎn)SKIPIF1<0，則下列正確的為（

）A．SKIPIF1<0在SKIPIF1<0單調(diào)遞減B．SKIPIF1<0的一條對(duì)稱軸為SKIPIF1<0C．SKIPIF1<0的最小正周期為SKIPIF1<0D．把函數(shù)SKIPIF1<0的圖像向左平移SKIPIF1<0個(gè)長(zhǎng)度單位得到函數(shù)SKIPIF1<0的解析式為SKIPIF1<010．（2022·吉林·東北師大附中模擬預(yù)測(cè)）將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度，向下平移SKIPIF1<0個(gè)單位長(zhǎng)度后，得到SKIPIF1<0的圖象，若對(duì)于任意的實(shí)數(shù)SKIPIF1<0，SKIPIF1<0都單調(diào)遞增，則正數(shù)SKIPIF1<0的值可能為（

）A．3 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（2022·福建寧德·高三期中）聲音是由物體振動(dòng)產(chǎn)生的聲波，其中包含著正弦函數(shù)，純音的數(shù)學(xué)模型是函數(shù)SKIPIF1<0，我們聽到的聲音是由純音合成的，稱之為復(fù)合音，若一個(gè)復(fù)合音的數(shù)學(xué)模型函數(shù)f（x），其圖象是由SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，再把所得圖象各點(diǎn)的橫坐標(biāo)縮短到原來的SKIPIF1<0倍，再把所得圖象各點(diǎn)的縱坐標(biāo)伸長(zhǎng)到原來的2倍而得到，若SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0的圖像關(guān)于點(diǎn)（SKIPIF1<0，0）中心對(duì)稱B．f（x）在SKIPIF1<0單調(diào)遞減C．若一個(gè)奇函數(shù)的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度后，可得f（x）的圖象，則n的最小值為SKIPIF1<0D．若SKIPIF1<0在SKIPIF1<0有解，則k的取值范圍是SKIPIF1<012．（2022·廣東·華南師大附中南海實(shí)驗(yàn)高中高三階段練習(xí)）已知函數(shù)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0，SKIPIF1<0