新高考數(shù)學二輪復(fù)習專題講測練專題15 周期性、單調(diào)性、奇偶性、對稱性的靈活運用（精講精練）（原卷版）

專題15周期性、單調(diào)性、奇偶性、對稱性的靈活運用【命題規(guī)律】從近五年的高考情況來看，本節(jié)是高考的一個重點，函數(shù)的單調(diào)性、奇偶性、周期性是高考的必考內(nèi)容，重點關(guān)注單調(diào)性、奇偶性結(jié)合在一起，與函數(shù)圖像、函數(shù)零點和不等式相結(jié)合進行考查，解題時要充分運用轉(zhuǎn)化思想和數(shù)形結(jié)合思想．【核心考點目錄】核心考點一：函數(shù)單調(diào)性的綜合應(yīng)用核心考點二：函數(shù)的奇偶性的綜合應(yīng)用核心考點三：已知SKIPIF1<0奇函數(shù)SKIPIF1<0核心考點四：利用軸對稱解決函數(shù)問題核心考點五：利用中心對稱解決函數(shù)問題核心考點六：利用周期性和對稱性解決函數(shù)問題核心考點七：類周期函數(shù)核心考點八：抽象函數(shù)的單調(diào)性、奇偶性、周期性、對稱性核心考點九：函數(shù)性質(zhì)的綜合【真題回歸】1．（2022·全國·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0的定義域為R，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．0 D．12．（2022·全國·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0的定義域均為R，且SKIPIF1<0．若SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對稱，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（多選題）（2022·全國·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0的定義域均為SKIPIF1<0，記SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0均為偶函數(shù)，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國·統(tǒng)考高考真題）若SKIPIF1<0是奇函數(shù)，則SKIPIF1<0_____，SKIPIF1<0______．【方法技巧與總結(jié)】1、單調(diào)性技巧（1）證明函數(shù)單調(diào)性的步驟①取值：設(shè)SKIPIF1<0，SKIPIF1<0是SKIPIF1<0定義域內(nèi)一個區(qū)間上的任意兩個量，且SKIPIF1<0；②變形：作差變形（變形方法：因式分解、配方、有理化等）或作商變形；③定號：判斷差的正負或商與SKIPIF1<0的大小關(guān)系；④得出結(jié)論．（2）函數(shù)單調(diào)性的判斷方法①定義法：根據(jù)增函數(shù)、減函數(shù)的定義，按照“取值—變形—判斷符號—下結(jié)論”進行判斷．②圖象法：就是畫出函數(shù)的圖象，根據(jù)圖象的上升或下降趨勢，判斷函數(shù)的單調(diào)性．③直接法：就是對我們所熟悉的函數(shù)，如一次函數(shù)、二次函數(shù)、反比例函數(shù)等，直接寫出它們的單調(diào)區(qū)間．（3）記住幾條常用的結(jié)論：①若SKIPIF1<0是增函數(shù)，則SKIPIF1<0為減函數(shù)；若SKIPIF1<0是減函數(shù)，則SKIPIF1<0為增函數(shù)；②若SKIPIF1<0和SKIPIF1<0均為增（或減）函數(shù)，則在SKIPIF1<0和SKIPIF1<0的公共定義域上SKIPIF1<0為增（或減）函數(shù)；③若SKIPIF1<0且SKIPIF1<0為增函數(shù)，則函數(shù)SKIPIF1<0為增函數(shù)，SKIPIF1<0為減函數(shù)；④若SKIPIF1<0且SKIPIF1<0為減函數(shù)，則函數(shù)SKIPIF1<0為減函數(shù)，SKIPIF1<0為增函數(shù)．2、奇偶性技巧（1）函數(shù)具有奇偶性的必要條件是其定義域關(guān)于原點對稱．（2）奇偶函數(shù)的圖象特征．函數(shù)SKIPIF1<0是偶函數(shù)SKIPIF1<0函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0軸對稱；函數(shù)SKIPIF1<0是奇函數(shù)SKIPIF1<0函數(shù)SKIPIF1<0的圖象關(guān)于原點中心對稱．（3）若奇函數(shù)SKIPIF1<0在SKIPIF1<0處有意義，則有SKIPIF1<0；偶函數(shù)SKIPIF1<0必滿足SKIPIF1<0．（4）偶函數(shù)在其定義域內(nèi)關(guān)于原點對稱的兩個區(qū)間上單調(diào)性相反；奇函數(shù)在其定義域內(nèi)關(guān)于原點對稱的兩個區(qū)間上單調(diào)性相同．（5）若函數(shù)SKIPIF1<0的定義域關(guān)于原點對稱，則函數(shù)SKIPIF1<0能表示成一個偶函數(shù)與一個奇函數(shù)的和的形式．記SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0．（6）運算函數(shù)的奇偶性規(guī)律：運算函數(shù)是指兩個（或多個）函數(shù)式通過加、減、乘、除四則運算所得的函數(shù)，如SKIPIF1<0．對于運算函數(shù)有如下結(jié)論：奇SKIPIF1<0奇=奇；偶SKIPIF1<0偶=偶；奇SKIPIF1<0偶=非奇非偶；奇SKIPIF1<0奇=偶；奇SKIPIF1<0偶=奇；偶SKIPIF1<0偶=偶．（7）復(fù)合函數(shù)SKIPIF1<0的奇偶性原來：內(nèi)偶則偶，兩奇為奇．（8）常見奇偶性函數(shù)模型奇函數(shù)：=1\*GB3①函數(shù)SKIPIF1<0或函數(shù)SKIPIF1<0．=2\*GB3②函數(shù)SKIPIF1<0．=3\*GB3③函數(shù)SKIPIF1<0或函數(shù)SKIPIF1<0=4\*GB3④函數(shù)SKIPIF1<0或函數(shù)SKIPIF1<0．注意：關(guān)于=1\*GB3①式，可以寫成函數(shù)SKIPIF1<0或函數(shù)SKIPIF1<0．偶函數(shù)：=1\*GB3①函數(shù)SKIPIF1<0．=2\*GB3②函數(shù)SKIPIF1<0．=3\*GB3③函數(shù)SKIPIF1<0類型的一切函數(shù)．④常數(shù)函數(shù)3、周期性技巧SKIPIF1<04、函數(shù)的的對稱性與周期性的關(guān)系（1）若函數(shù)SKIPIF1<0有兩條對稱軸SKIPIF1<0，SKIPIF1<0，則函數(shù)SKIPIF1<0是周期函數(shù)，且SKIPIF1<0；（2）若函數(shù)SKIPIF1<0的圖象有兩個對稱中心SKIPIF1<0，則函數(shù)SKIPIF1<0是周期函數(shù)，且SKIPIF1<0；（3）若函數(shù)SKIPIF1<0有一條對稱軸SKIPIF1<0和一個對稱中心SKIPIF1<0，則函數(shù)SKIPIF1<0是周期函數(shù)，且SKIPIF1<0．5、對稱性技巧（1）若函數(shù)SKIPIF1<0關(guān)于直線SKIPIF1<0對稱，則SKIPIF1<0．（2）若函數(shù)SKIPIF1<0關(guān)于點SKIPIF1<0對稱，則SKIPIF1<0．（3）函數(shù)SKIPIF1<0與SKIPIF1<0關(guān)于SKIPIF1<0軸對稱，函數(shù)SKIPIF1<0與SKIPIF1<0關(guān)于原點對稱．【核心考點】核心考點一：函數(shù)單調(diào)性的綜合應(yīng)用【典型例題】例1．（2023春·江西鷹潭·高三貴溪市實驗中學?？茧A段練習）已知函數(shù)SKIPIF1<0是SKIPIF1<0上的減函數(shù)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例2．（2023·全國·高三專題練習）設(shè)函數(shù)SKIPIF1<0，則滿足SKIPIF1<0的SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例3．（2023·全國·高三專題練習）已知SKIPIF1<0，且滿足SKIPIF1<0，則下列正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0核心考點二：函數(shù)的奇偶性的綜合應(yīng)用【典型例題】例4．（2023·全國·高三專題練習）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，且SKIPIF1<0為偶函數(shù)，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例5．（2023·全國·高三專題練習）設(shè)SKIPIF1<0是定義在R上的奇函數(shù)，且當SKIPIF1<0時，SKIPIF1<0，不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例6．（2023·全國·高三專題練習）已知偶函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，且當SKIPIF1<0時，SKIPIF1<0，則使不等式SKIPIF1<0成立的實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例7．（2023·全國·高三專題練習）定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，且SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例8．（2023春·廣西·高三期末）SKIPIF1<0是定義在R上的函數(shù)，SKIPIF1<0為奇函數(shù)，則SKIPIF1<0（

）A．－1 B．SKIPIF1<0 C．SKIPIF1<0 D．1例9．（2023春·甘肅蘭州·高三蘭化一中?？茧A段練習）若函數(shù)f（x）=SKIPIF1<0，則滿足SKIPIF1<0恒成立的實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點三：已知SKIPIF1<0奇函數(shù)+M【典型例題】例10．（2022·重慶一中高三階段練習）已知SKIPIF1<0（a，b為實數(shù)），SKIPIF1<0，則SKIPIF1<0______．例11．（2022·河南·西平縣高級中學模擬預(yù)測（理））已知函數(shù)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．2 B．3 C．－2 D．－3例12．（2022·福建省福州第一中學高二期末）若對SKIPIF1<0，有SKIPIF1<0，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在最大值和最小值，則其最大值與最小值的和為（）A．4 B．8 C．12 D．16核心考點四：利用軸對稱解決函數(shù)問題【典型例題】例13．（2022·全國·高三專題練習）若SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0等于（

）A．2 B．3 C．4 D．5例14．（2021春·高一單元測試）設(shè)函數(shù)SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．（0，2] B．SKIPIF1<0C．[2，＋∞） D．SKIPIF1<0∪[2，＋∞）例15．（2021春·西藏拉薩·高三?？茧A段練習）已知函數(shù)SKIPIF1<0，則SKIPIF1<0的大小關(guān)系（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0核心考點五：利用中心對稱解決函數(shù)問題【典型例題】例16．（2023·全國·高三專題練習）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．SKIPIF1<0例17．（2021春·安徽六安·高三?？茧A段練習）已知函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0為奇函數(shù)，若函數(shù)SKIPIF1<0與SKIPIF1<0圖象共有SKIPIF1<0個交點為SKIPIF1<0、SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例18．（2021春·貴州黔東南·高一凱里一中?？计谥校┮阎瘮?shù)SKIPIF1<0是奇函數(shù)，若函數(shù)SKIPIF1<0與SKIPIF1<0圖象的交點分別為SKIPIF1<0，SKIPIF1<0，…，SKIPIF1<0，則交點的所有橫坐標和縱坐標之和為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例19．（2022春·湖北恩施·高一恩施市第一中學?？茧A段練習）已知定義在R上的奇函數(shù)SKIPIF1<0的圖象與SKIPIF1<0軸交點的橫坐標分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例20．（2021春·四川綿陽·高一四川省綿陽南山中學?？茧A段練習）已知函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0滿足SKIPIF1<0，若函數(shù)SKIPIF1<0恰有SKIPIF1<0個零點，則所有這些零點之和為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點六：利用周期性和對稱性解決函數(shù)問題【典型例題】例21．（2023·全國·高三專題練習）已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，SKIPIF1<0為偶函數(shù)，SKIPIF1<0為奇函數(shù)，且當SKIPIF1<0時，SKIPIF1<0．若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．SKIPIF1<0 D．SKIPIF1<0例22．（2023·四川資陽·統(tǒng)考模擬預(yù)測）已知函數(shù)SKIPIF1<0的定義域為R，SKIPIF1<0為偶函數(shù)，SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0（SKIPIF1<0且SKIPIF1<0），且SKIPIF1<0．則SKIPIF1<0（

）A．16 B．20 C．24 D．28例23．（2023·山東濟寧·高三嘉祥縣第一中學?？茧A段練習）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．若直線SKIPIF1<0與曲線SKIPIF1<0恰有三個公共點，那么實數(shù)a的取值的集合為（

）A．SKIPIF1<0（SKIPIF1<0） B．SKIPIF1<0（SKIPIF1<0）C．SKIPIF1<0（SKIPIF1<0） D．SKIPIF1<0（SKIPIF1<0）例24．（2023·全國·高三專題練習）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，若函數(shù)SKIPIF1<0圖象與SKIPIF1<0的圖象恰有10個不同的公共點，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例25．（2023春·江西鷹潭·高三貴溪市實驗中學?？茧A段練習）已知SKIPIF1<0是定義在R上的奇函數(shù)，SKIPIF1<0，恒有SKIPIF1<0，且當SKIPIF1<0時，SKIPIF1<01，則SKIPIF1<0（

）A．1 B．-1 C．0 D．2例26．（2023·山東濟寧·高三嘉祥縣第一中學?？茧A段練習）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．若直線SKIPIF1<0與曲線SKIPIF1<0恰有三個公共點，那么實數(shù)a的取值的集合為（

）A．SKIPIF1<0（SKIPIF1<0） B．SKIPIF1<0（SKIPIF1<0）C．SKIPIF1<0（SKIPIF1<0） D．SKIPIF1<0（SKIPIF1<0）例27．（2023·全國·高三專題練習）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，若函數(shù)SKIPIF1<0圖象與SKIPIF1<0的圖象恰有10個不同的公共點，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例28．（2023春·江西鷹潭·高三貴溪市實驗中學?？茧A段練習）已知SKIPIF1<0是定義在R上的奇函數(shù)，SKIPIF1<0，恒有SKIPIF1<0，且當SKIPIF1<0時，SKIPIF1<01，則SKIPIF1<0（

）A．1 B．-1 C．0 D．2核心考點七：類周期函數(shù)【典型例題】例29．（2022·天津一中高三月考）定義域為SKIPIF1<0的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0，若當SKIPIF1<0時，不等式SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例30．（2022·浙江·杭州高級中學高三期中）定義域為SKIPIF1<0的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0，若SKIPIF1<0時，SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例31．（2022山西省榆林市高三二模理科數(shù)學試卷）定義域為SKIPIF1<0的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0，若當SKIPIF1<0時，函數(shù)SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的取值范圍為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點八：抽象函數(shù)的單調(diào)性、奇偶性、周期性、對稱性【典型例題】例32．（2023·廣東·高三統(tǒng)考學業(yè)考試）已知函數(shù)SKIPIF1<0對任意SKIPIF1<0，都有SKIPIF1<0成立．有以下結(jié)論：①SKIPIF1<0；②SKIPIF1<0是SKIPIF1<0上的偶函數(shù)；③若SKIPIF1<0，則SKIPIF1<0；④當SKIPIF1<0時，恒有SKIPIF1<0，則函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增．則上述所有正確結(jié)論的編號是________例33．（2022·山東聊城·二模）已知SKIPIF1<0為SKIPIF1<0上的奇函數(shù)，SKIPIF1<0，若對SKIPIF1<0，SKIPIF1<0，當SKIPIF1<0時，都有SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例34．（2022·全國·模擬預(yù)測（理））已知定義在R上的奇函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，且SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例35．（2022·黑龍江大慶·三模（理））已知定義域為R的偶函數(shù)滿足SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0，則方程SKIPIF1<0在區(qū)間SKIPIF1<0上所有解的和為（

）A．8 B．7 C．6 D．5【典型例題】例36．（2023·上海·高三專題練習）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，在SKIPIF1<0上是增函數(shù)，且SKIPIF1<0恒成立，則不等式SKIPIF1<0的解集為______．例37．（2023春·山東濟南·高三統(tǒng)考期中）已知SKIPIF1<0是定義域為R的奇函數(shù)，SKIPIF1<0為奇函數(shù)，則SKIPIF1<0__________．例38．（2023春·重慶璧山·高三校聯(lián)考階段練習）設(shè)a＞0，b＞0，若關(guān)于x的方程SKIPIF1<0恰有三個不同的實數(shù)解x1，x2，x3，且x1＜x2＜x3＝b，則a+b的值為______．例39．（2023·全國·高三專題練習）已知SKIPIF1<0是SKIPIF1<0上的偶函數(shù)，對于任意的SKIPIF1<0，均有SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0，則函數(shù)SKIPIF1<0的所有零點之和為______；【新題速遞】一、單選題1．（2023春·江西·高三校聯(lián)考階段練習）己知函數(shù)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0與SKIPIF1<0圖像的公共點個數(shù)為n，且這些公共點的橫坐標從小到大依次為SKIPIF1<0，SKIPIF1<0，…，SKIPIF1<0，則下列說法正確的有（

）個①若SKIPIF1<0，則SKIPIF1<0

②若SKIPIF1<0，則SKIPIF1<0③若SKIPIF1<0，則SKIPIF1<0

④若SKIPIF1<0，則SKIPIF1<0A．1 B．2 C．3 D．42．（2023·青海海東·統(tǒng)考一模）已知函數(shù)SKIPIF1<0SKIPIF1<0，且SKIPIF1<0，則下列結(jié)論正確的是（

）A．當SKIPIF1<0時，SKIPIF1<0在SKIPIF1<0上是增函數(shù)B．當SKIPIF1<0時，SKIPIF1<0在SKIPIF1<0上是增函數(shù)C．SKIPIF1<0的單調(diào)性與SKIPIF1<0有關(guān)D．若不等式SKIPIF1<0的解集是SKIPIF1<0，則SKIPIF1<03．（2023·青海海東·統(tǒng)考一模）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，若SKIPIF1<0，且SKIPIF1<0，則不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023春·重慶·高三統(tǒng)考階段練習）已知函數(shù)SKIPIF1<0，正實數(shù)a，b滿足SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．1 B．2 C．4 D．SKIPIF1<05．（2023春·江西鷹潭·高三貴溪市實驗中學?？茧A段練習）若正實數(shù)SKIPIF1<0滿足SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2023春·江西·高三校聯(lián)考階段練習）已知f（x），g（x）分別為定義域為R的偶函數(shù)和奇函數(shù)，且SKIPIF1<0，若關(guān)于x的不等式SKIPIF1<0在（0，ln2）上恒成立，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023春·江蘇南京·高三統(tǒng)考階段練習）設(shè)SKIPIF1<0，函數(shù)SKIPIF1<0是定義在R上的奇函數(shù)，且SKIPIF1<0，SKIPIF1<0在SKIPIF1<0單調(diào)遞增，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2023春·遼寧·高三校聯(lián)考期中）已知偶函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，則滿足SKIPIF1<0的x的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．（2023春·福建寧德·高三?？茧A段練習）已知函數(shù)SKIPIF1<0的定義域為R，SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)，且SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0為偶函數(shù)，則下列一定成立的有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．（2023春·廣東廣州·高三統(tǒng)考階段練習）已知函數(shù)SKIPIF1<0、SKIPIF1<0的定義域均為SKIPIF1<0，SKIPIF1<0為偶函數(shù)，且SKIPIF1<0，SKIPIF1<0，下列說法正確的有（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0對稱 B．函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0對稱C．函數(shù)SKIPIF1<0是以SKIPIF1<0為周期的周期函數(shù) D．函數(shù)SKIPIF1<0是以SKIPIF1<0為周期的周期函數(shù)11．（