高考數(shù)學二輪復習核心專題講練：函數(shù)與導數(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：知識強化第二部分：重難點題型突破突破一：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)奇偶性與對稱性與周期性綜合突破四：函數(shù)的圖象及其應用角度1：根據(jù)解析式識別函數(shù)圖象角度2由圖象確定函數(shù)解析式

第三部分：沖刺重難點特訓第一部分：知識強化1、函數(shù)的單調(diào)性①判斷方法:定義法、圖象法、導數(shù)法.②復合函數(shù)的單調(diào)性（同調(diào)增；異調(diào)減）對于函數(shù)SKIPIF1<0和SKIPIF1<0，如果當SKIPIF1<0時，SKIPIF1<0，且SKIPIF1<0在區(qū)間SKIPIF1<0上和SKIPIF1<0在區(qū)間SKIPIF1<0上同時具有單調(diào)性，則復合函數(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SKIPIF1<0，兩個函數(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對數(shù)型復合函數(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)周期性的常用結論與技巧（同號周期）設函數(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)對稱性（1）軸對稱：若函數(shù)SKIPIF1<0關于直線SKIPIF1<0對稱，則①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0（2）點對稱：若函數(shù)SKIPIF1<0關于直線SKIPIF1<0對稱，則①SKIPIF1<0②SKIPIF1<0③SKIPIF1<0（2）點對稱：若函數(shù)SKIPIF1<0關于直線SKIPIF1<0對稱，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軸左側的圖象，保留SKIPIF1<0軸右側的圖象；將SKIPIF1<0軸右側圖象翻折到SKIPIF1<0軸左側；本質(zhì)是個偶函數(shù)）（5）圖象識別技巧（按使用頻率優(yōu)先級排序）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；）⑤零點法⑥極大值極小值法第二部分：重難點題型突破突破一：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)學校模擬預測）已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，則函數(shù)SKIPIF1<0的定義域為（

）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·江西科技學院附屬中學模擬預測（文））函數(shù)SKIPIF1<0的值域（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·上海市光明中學模擬預測）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SKIPIF1<0的值域為SKIPIF1<0．若存在實數(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)及其應用1．（2022·廣東·深圳市光明區(qū)高級中學模擬預測）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·上饒市第一中學模擬預測（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·模擬預測（文））已知函數(shù)SKIPIF1<0若函數(shù)SKIPIF1<0有三個零點，則實數(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測（文））已知函數(shù)SKIPIF1<0滿足對任意的實數(shù)SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0成立，則實數(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測（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)大學附屬中學模擬預測（理））已知函數(shù)SKIPIF1<0，則SKIPIF1<0的圖象上關于坐標原點SKIPIF1<0對稱的點共有（

）A．0對 B．1對 C．2對 D．3對突破二：函數(shù)奇偶性與單調(diào)性1．（2022·河南·模擬預測（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·開封市東信學校模擬預測（文））已知SKIPIF1<0是SKIPIF1<0上的奇函數(shù)，當SKIPIF1<0時，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·通許縣第一高級中學模擬預測（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的定義域為SKIPIF1<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)外國語高級中學有限公司模擬預測）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)外國語高級中學有限公司模擬預測）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·固始縣高級中學第一中學模擬預測（文））已知函數(shù)SKIPIF1<0是SKIPIF1<0上的偶函數(shù)，且SKIPIF1<0的圖象關于點SKIPIF1<0對稱，當SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．23．（2022·四川·鹽亭中學模擬預測（文））已知定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，當SKIPIF1<0時，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的定義域為SKIPIF1<0,且SKIPIF1<0對任意SKIPIF1<0恒成立,若SKIPIF1<0,則SKIPIF1<0____________.6．（2022·遼寧·東北育才雙語學校一模）已知函數(shù)SKIPIF1<0的圖象關于直線SKIPIF1<0對稱，且對SKIPIF1<0都有SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0.則SKIPIF1<0___________.突破四：函數(shù)的圖象及其應用角度1：根據(jù)解析式識別函數(shù)圖象1．（2022·四川雅安·模擬預測（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·模擬預測）函數(shù)SKIPIF1<0的部分圖像大致為（

）A． B．C． D．3．（2022·河南省葉縣高級中學模擬預測（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測）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預測（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)大學附屬中學模擬預測（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·金華市曙光學校模擬預測）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·安慶一中模擬預測（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：沖刺重難點特訓一、單選題1．（2022·遼寧實驗中學高一期中）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）對于定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，如果存在實數(shù)SKIPIF1<0，使得SKIPIF1<0對任意實數(shù)SKIPIF1<0恒成立，則稱SKIPIF1<0為關于SKIPIF1<0的“SKIPIF1<0函數(shù)”．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0是關于SKIPIF1<0和SKIPIF1<0的“SKIPIF1<0函數(shù)”，且當SKIPIF1<0時SKIPIF1<0的值域為SKIPIF1<0，則當SKIPIF1<0時SKIPIF1<0的值域為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·廣東·深圳市寶安中學（集團）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·德清縣教育研訓中心高一期中）已知SKIPIF1<0是偶函數(shù)，對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．（2022·四川外國語大學附屬外國語學校高一期中）已知函數(shù)SKIPIF1<0，若對所有SKIPIF1<0，都有SKIPIF1<0成立，則實數(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）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足：SKIPIF1<0．且當SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·黑龍江·牡丹江市第二高級中學高三階段練習）函數(shù)SKIPIF1<0對任意SKIPIF1<0都有SKIPIF1<0成立，且函數(shù)SKIPIF1<0的圖象關于點SKIPIF1<0對稱，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SKIPIF1<0時，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SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．2 D．311．（2022·廣東·深圳市福田區(qū)福田中學高三階段練習）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·模擬預測（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·唐山市第十一中學高三階段練習）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…為自然對數(shù)的底數(shù)）與所給圖像最契合的是（

）A．SKIPIF1<0 B．SKIPIF1<0