高考數(shù)學(xué)二輪復(fù)習(xí)核心專題講練：函數(shù)與導(dǎo)數(shù)第1講 函數(shù)的圖象與性質(zhì) 原卷版

第1講函數(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：函數(shù)的定義及其表示角度1：函數(shù)的定義域角度2：函數(shù)的值域角度3：分段函數(shù)及其應(yīng)用突破二：函數(shù)奇偶性與單調(diào)性突破三：函數(shù)奇偶性與對(duì)稱性與周期性綜合突破四：函數(shù)的圖象及其應(yīng)用角度1：根據(jù)解析式識(shí)別函數(shù)圖象角度2由圖象確定函數(shù)解析式

第三部分：沖刺重難點(diǎn)特訓(xùn)第一部分：知識(shí)強(qiáng)化1、函數(shù)的單調(diào)性①判斷方法:定義法、圖象法、導(dǎo)數(shù)法.②復(fù)合函數(shù)的單調(diào)性（同調(diào)增；異調(diào)減）對(duì)于函數(shù)SKIPIF1<0和SKIPIF1<0，如果當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，且SKIPIF1<0在區(qū)間SKIPIF1<0上和SKIPIF1<0在區(qū)間SKIPIF1<0上同時(shí)具有單調(diào)性，則復(fù)合函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上具有單調(diào)性，并且具有這樣的規(guī)律：增增(或減減)則增，增減(或減增)則減．③函數(shù)相加或相減后單調(diào)性設(shè)SKIPIF1<0，兩個(gè)函數(shù)SKIPIF1<0，SKIPIF1<0在區(qū)間SKIPIF1<0上的單調(diào)性如下表，則SKIPIF1<0在SKIPIF1<0上的單調(diào)性遵循（增+增=增；減+減=減）SKIPIF1<0SKIPIF1<0SKIPIF1<0增增增減減減SKIPIF1<0SKIPIF1<0SKIPIF1<0增減增減增減2、函數(shù)的奇偶性①判斷方法:定義法、圖象法、奇偶函數(shù)性質(zhì)法(如奇函數(shù)×奇函數(shù)是偶函數(shù)).②對(duì)數(shù)型復(fù)合函數(shù)判斷奇偶性常用SKIPIF1<0或SKIPIF1<0來判斷奇偶性.③SKIPIF1<0，SKIPIF1<0在它們的公共定義域上有下面的結(jié)論：SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0偶函數(shù)偶函數(shù)偶函數(shù)偶函數(shù)偶函數(shù)偶函數(shù)偶函數(shù)奇函數(shù)不能確定不能確定奇函數(shù)奇函數(shù)奇函數(shù)偶函數(shù)不能確定不能確定奇函數(shù)奇函數(shù)奇函數(shù)奇函數(shù)奇函數(shù)奇函數(shù)偶函數(shù)偶函數(shù)3、函數(shù)的周期性函數(shù)周期性的常用結(jié)論與技巧（同號(hào)周期）設(shè)函數(shù)SKIPIF1<0，SKIPIF1<0.①若SKIPIF1<0，則函數(shù)的周期SKIPIF1<0；②若SKIPIF1<0，則函數(shù)的周期SKIPIF1<0；③若SKIPIF1<0，則函數(shù)的周期SKIPIF1<0；④若SKIPIF1<0，則函數(shù)的周期SKIPIF1<0；⑤SKIPIF1<0，則函數(shù)的周期SKIPIF1<04、函數(shù)對(duì)稱性（1）軸對(duì)稱：若函數(shù)SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱，則①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0（2）點(diǎn)對(duì)稱：若函數(shù)SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱，則①SKIPIF1<0②SKIPIF1<0③SKIPIF1<0（2）點(diǎn)對(duì)稱：若函數(shù)SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱，則①SKIPIF1<0②SKIPIF1<0③SKIPIF1<05、函數(shù)圖象（1）平移變換（左“+”右“-”；上“+”下“-”）①SKIPIF1<0②SKIPIF1<0③SKIPIF1<0④SKIPIF1<0（2）對(duì)稱變換①SKIPIF1<0的圖象SKIPIF1<0SKIPIF1<0的圖象；②SKIPIF1<0的圖象SKIPIF1<0SKIPIF1<0的圖象；③SKIPIF1<0的圖象SKIPIF1<0SKIPIF1<0的圖象；④SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)的圖象SKIPIF1<0SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)的圖象.（3）伸縮變換①SKIPIF1<0SKIPIF1<0SKIPIF1<0.②SKIPIF1<0SKIPIF1<0SKIPIF1<0.（4）翻折變換（絕對(duì)值變換）①SKIPIF1<0的圖象SKIPIF1<0SKIPIF1<0的圖象；（口訣；以SKIPIF1<0軸為界，保留SKIPIF1<0軸上方的圖象；將SKIPIF1<0軸下方的圖象翻折到SKIPIF1<0軸上方）②SKIPIF1<0的圖象SKIPIF1<0SKIPIF1<0的圖象.（口訣；以SKIPIF1<0軸為界，去掉SKIPIF1<0軸左側(cè)的圖象，保留SKIPIF1<0軸右側(cè)的圖象；將SKIPIF1<0軸右側(cè)圖象翻折到SKIPIF1<0軸左側(cè)；本質(zhì)是個(gè)偶函數(shù)）（5）圖象識(shí)別技巧（按使用頻率優(yōu)先級(jí)排序）①特殊值法（觀察圖象，尋找圖象中出現(xiàn)的特殊值）②單調(diào)性法（SKIPIF1<0；SKIPIF1<0；SKIPIF1<0，SKIPIF1<0；通過求導(dǎo)判斷單調(diào)性）③奇偶性法SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0偶函數(shù)偶函數(shù)偶函數(shù)偶函數(shù)偶函數(shù)偶函數(shù)偶函數(shù)奇函數(shù)不能確定不能確定奇函數(shù)奇函數(shù)奇函數(shù)偶函數(shù)不能確定不能確定奇函數(shù)奇函數(shù)奇函數(shù)奇函數(shù)奇函數(shù)奇函數(shù)偶函數(shù)偶函數(shù)④極限（左右極限）（SKIPIF1<0；SKIPIF1<0；SKIPIF1<0；SKIPIF1<0；）⑤零點(diǎn)法⑥極大值極小值法第二部分：重難點(diǎn)題型突破突破一：函數(shù)的定義及其表示角度1：函數(shù)的定義域1．（2022·山東濟(jì)南·二模）函數(shù)SKIPIF1<0的定義域是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·江西·修水中等專業(yè)學(xué)校模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，則函數(shù)SKIPIF1<0的定義域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0角度2：函數(shù)的值域1．（2022·全國·江西科技學(xué)院附屬中學(xué)模擬預(yù)測(cè)（文））函數(shù)SKIPIF1<0的值域（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·上海市光明中學(xué)模擬預(yù)測(cè)）已知定義在SKIPIF1<0的函數(shù)SKIPIF1<0，滿足：SKIPIF1<0在SKIPIF1<0上的解析式為SKIPIF1<0，設(shè)SKIPIF1<0的值域?yàn)镾KIPIF1<0．若存在實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的可能取值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0角度3：分段函數(shù)及其應(yīng)用1．（2022·廣東·深圳市光明區(qū)高級(jí)中學(xué)模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·江西·上饒市第一中學(xué)模擬預(yù)測(cè)（理））已知SKIPIF1<0，若SKIPIF1<0，則n的最大值為（

）A．9 B．10 C．11 D．123．（2022·山西·模擬預(yù)測(cè)（文））已知函數(shù)SKIPIF1<0若函數(shù)SKIPIF1<0有三個(gè)零點(diǎn)，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·河南省杞縣高中模擬預(yù)測(cè)（文））已知函數(shù)SKIPIF1<0滿足對(duì)任意的實(shí)數(shù)SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·全國·江西師大附中模擬預(yù)測(cè)（文））已知函數(shù)SKIPIF1<0則不等式SKIPIF1<0的解集為______．6．（2022·陜西·西北工業(yè)大學(xué)附屬中學(xué)模擬預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0，則SKIPIF1<0的圖象上關(guān)于坐標(biāo)原點(diǎn)SKIPIF1<0對(duì)稱的點(diǎn)共有（

）A．0對(duì) B．1對(duì) C．2對(duì) D．3對(duì)突破二：函數(shù)奇偶性與單調(diào)性1．（2022·河南·模擬預(yù)測(cè)（理））已知SKIPIF1<0是偶函數(shù)且在SKIPIF1<0上單調(diào)遞增，則滿足SKIPIF1<0的一個(gè)區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南·開封市東信學(xué)校模擬預(yù)測(cè)（文））已知SKIPIF1<0是SKIPIF1<0上的奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則滿足SKIPIF1<0的m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·河南·通許縣第一高級(jí)中學(xué)模擬預(yù)測(cè)（文））已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，且SKIPIF1<0上單調(diào)遞減，設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·廣西北?！ひ荒＃ɡ恚┮阎婧瘮?shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，且SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，在SKIPIF1<0上單調(diào)遞減．若SKIPIF1<0，則SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·河南許昌·三模（文））已知函數(shù)SKIPIF1<0是定義在R上的偶函數(shù)，且在區(qū)間SKIPIF1<0上是減函數(shù)，SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·青?！の鲗幈蓖飧綄傩氯A聯(lián)外國語高級(jí)中學(xué)有限公司模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，則不等式SKIPIF1<0的解集為______．突破三：函數(shù)奇偶性與對(duì)稱性與周期性綜合1．（2022·青?！の鲗幈蓖飧綄傩氯A聯(lián)外國語高級(jí)中學(xué)有限公司模擬預(yù)測(cè)）已知定義域是R的函數(shù)SKIPIF1<0滿足：SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為偶函數(shù)，SKIPIF1<0，則SKIPIF1<0（

）A．1 B．-1 C．2 D．-32．（2022·河南·固始縣高級(jí)中學(xué)第一中學(xué)模擬預(yù)測(cè)（文））已知函數(shù)SKIPIF1<0是SKIPIF1<0上的偶函數(shù)，且SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．23．（2022·四川·鹽亭中學(xué)模擬預(yù)測(cè)（文））已知定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0（

）A．3 B．0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·河南信陽·一模（理））已知定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·廣西北?！ひ荒＃ㄎ模┮阎婧瘮?shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0,且SKIPIF1<0對(duì)任意SKIPIF1<0恒成立,若SKIPIF1<0,則SKIPIF1<0____________.6．（2022·遼寧·東北育才雙語學(xué)校一模）已知函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱，且對(duì)SKIPIF1<0都有SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.則SKIPIF1<0___________.突破四：函數(shù)的圖象及其應(yīng)用角度1：根據(jù)解析式識(shí)別函數(shù)圖象1．（2022·四川雅安·模擬預(yù)測(cè)（理））函數(shù)SKIPIF1<0在SKIPIF1<0上的圖象大致是（

）A． B．C． D．2．（2022·江蘇南通·模擬預(yù)測(cè)）函數(shù)SKIPIF1<0的部分圖像大致為（

）A． B．C． D．3．（2022·河南省葉縣高級(jí)中學(xué)模擬預(yù)測(cè)（文））函數(shù)SKIPIF1<0在SKIPIF1<0的圖像大致為（

）A． B．C． D．4．（2022·黑龍江·雞東縣第二中學(xué)二模）函數(shù)SKIPIF1<0的大致圖象是（

）A． B．C． D．5．（2022·吉林·東北師大附中模擬預(yù)測(cè)）函數(shù)SKIPIF1<0的大致圖象是（

）A． B．C． D．角度2由圖象確定函數(shù)解析式

1．（2022·青?！つM預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0的部分圖像如圖所示，則函數(shù)SKIPIF1<0的解析式可能為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·陜西·西北工業(yè)大學(xué)附屬中學(xué)模擬預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0圖象如圖所示，那么該函數(shù)可能為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·浙江·金華市曙光學(xué)校模擬預(yù)測(cè)）函數(shù)SKIPIF1<0的圖像如圖所示,則其解析式可能是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·安徽·安慶一中模擬預(yù)測(cè)（文））已知函數(shù)SKIPIF1<0在SKIPIF1<0上的圖象如圖所示，則函數(shù)SKIPIF1<0的解析式可能為（

）SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·黑龍江·一模（理））已知某個(gè)函數(shù)的圖像如圖所示，則下列解析式中與此圖像最為符合的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0第三部分：沖刺重難點(diǎn)特訓(xùn)一、單選題1．（2022·遼寧實(shí)驗(yàn)中學(xué)高一期中）函數(shù)SKIPIF1<0的值域是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·浙江·溫州中學(xué)高一期中）函數(shù)SKIPIF1<0的值域是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·江西·高二階段練習(xí)）對(duì)于定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，如果存在實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0對(duì)任意實(shí)數(shù)SKIPIF1<0恒成立，則稱SKIPIF1<0為關(guān)于SKIPIF1<0的“SKIPIF1<0函數(shù)”．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0是關(guān)于SKIPIF1<0和SKIPIF1<0的“SKIPIF1<0函數(shù)”，且當(dāng)SKIPIF1<0時(shí)SKIPIF1<0的值域?yàn)镾KIPIF1<0，則當(dāng)SKIPIF1<0時(shí)SKIPIF1<0的值域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·廣東·深圳市寶安中學(xué)（集團(tuán)）高一期中）已知函數(shù)SKIPIF1<0的最小值為SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0D．SKIPIF1<05．（2022·浙江·德清縣教育研訓(xùn)中心高一期中）已知SKIPIF1<0是偶函數(shù)，對(duì)SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0，且SKIPIF1<0則SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·四川外國語大學(xué)附屬外國語學(xué)校高一期中）已知函數(shù)SKIPIF1<0，若對(duì)所有SKIPIF1<0，都有SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·山西忻州·高三階段練習(xí)）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足：SKIPIF1<0．且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·黑龍江·牡丹江市第二高級(jí)中學(xué)高三階段練習(xí)）函數(shù)SKIPIF1<0對(duì)任意SKIPIF1<0都有SKIPIF1<0成立，且函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱，SKIPIF1<0，則SKIPIF1<0（

）A．4 B．3 C．2 D．19．（2022·河南南陽·高三期中（理））已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足：SKIPIF1<0，SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2022·貴州遵義·高三期中（理））已知定義在R上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．2 D．311．（2022·廣東·深圳市福田區(qū)福田中學(xué)高三階段練習(xí)）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0的圖象大致為（）A． B．C． D．12．（2022·河南·模擬預(yù)測(cè)（理））如圖是函數(shù)SKIPIF1<0的圖象，則函數(shù)SKIPIF1<0的解析式可以為（

）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<013．（2022·江蘇·南京師大附中高三期中）函數(shù)SKIPIF1<0的圖象大致為（

）A． B．C． D．14．（2022·河北·唐山市第十一中學(xué)高三階段練習(xí)）函數(shù)SKIPIF1<0的部分圖象大致為（

）A． B．C． D．15．（2022·遼寧大連·高三期中）下列函數(shù)的解析式（其中SKIPIF1<0…為自然對(duì)數(shù)的底數(shù)）與所給圖像最契合的是（

）A．SKIPIF1<0 B．SKIPIF1<0