新高考數(shù)學(xué)一輪復(fù)習(xí) 函數(shù)專項重難點突破專題11 函數(shù)的奇偶性、對稱性和周期性綜合(原卷版)

專題11函數(shù)的奇偶性、對稱性和周期性綜合考點一奇偶性與周期性一、單選題1．設(shè)SKIPIF1<0是定義域為R的奇函數(shù)，且SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．SKIPIF1<0是定義域為R的奇函數(shù)，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．3 B．SKIPIF1<0 C．6 D．03．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，SKIPIF1<0分別為函數(shù)SKIPIF1<0，SKIPIF1<0的導(dǎo)函數(shù)，若SKIPIF1<0為偶函數(shù)，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．2023 B．4 C．SKIPIF1<0 D．04．已知函數(shù)SKIPIF1<0定義域為SKIPIF1<0，對SKIPIF1<0，恒有SKIPIF1<0，則下列說法錯誤的有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．若SKIPIF1<0，則SKIPIF1<0周期為SKIPIF1<05．已知函數(shù)SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0的定義域均為SKIPIF1<0，SKIPIF1<0是偶函數(shù)，記SKIPIF1<0，SKIPIF1<0也是偶函數(shù)，則SKIPIF1<0的值為（

）A．-2 B．0 C．-1 D．2二、多選題6．已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，SKIPIF1<0是奇函數(shù)，SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．定義在R上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0時，SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，且SKIPIF1<0是奇函數(shù)，SKIPIF1<0是偶函數(shù)，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空題10．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0為偶函數(shù)，則SKIPIF1<0______.11．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，對任意實數(shù)SKIPIF1<0有SKIPIF1<0，若函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，SKIPIF1<0，則SKIPIF1<0______．12．定義在SKIPIF1<0的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的零點個數(shù)為______.13．已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且滿足SKIPIF1<0，又當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0______.14．已知定義R上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，又SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱，且SKIPIF1<0，則SKIPIF1<0______考點二奇偶性與對稱性一、單選題1．已知SKIPIF1<0是SKIPIF1<0上的偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0（

）A．1.4 B．3.4 C．1.6 D．3.62．設(shè)函數(shù)SKIPIF1<0的定義域為R，且SKIPIF1<0是奇函數(shù)，則SKIPIF1<0圖像（

）A．關(guān)于點SKIPIF1<0中心對稱 B．關(guān)于點SKIPIF1<0中心對稱C．關(guān)于直線SKIPIF1<0對稱 D．關(guān)于直線SKIPIF1<0對稱3．已知函數(shù)SKIPIF1<0，SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0，SKIPIF1<0的定義域均為SKIPIF1<0，SKIPIF1<0為奇函數(shù)，SKIPIF1<0關(guān)于直線SKIPIF1<0對稱，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0為奇函數(shù)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2022 D．20235．已知函數(shù)SKIPIF1<0是定義域為SKIPIF1<0的偶函數(shù)，且SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則關(guān)于SKIPIF1<0的方程SKIPIF1<0在SKIPIF1<0上所有實數(shù)解之和為（

）A．10 B．11 C．12 D．136．已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，若SKIPIF1<0，則SKIPIF1<0的值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知SKIPIF1<0是定義在SKIPIF1<0上的函數(shù),SKIPIF1<0為奇函數(shù),若函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0圖象交點的橫坐標(biāo)從小到大依次為SKIPIF1<0,則SKIPIF1<0（

）A．4 B．5 C．6 D．78．函數(shù)SKIPIF1<0的圖像關(guān)于點SKIPIF1<0成中心對稱的充要條件是函數(shù)SKIPIF1<0為奇函數(shù)，以下選項不正確的有（

）A．SKIPIF1<0關(guān)于SKIPIF1<0中心對稱B．SKIPIF1<0關(guān)于SKIPIF1<0中心對稱C．函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱，則SKIPIF1<0D．函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0對稱的充要條件是SKIPIF1<0為偶函數(shù)二、多選題9．已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，則（

）A．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱 B．SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱C．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱 D．SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱10．已知定義域為SKIPIF1<0的函數(shù)SKIPIF1<0滿足SKIPIF1<0不恒為零，且SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0是奇函數(shù)C．SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對稱 D．SKIPIF1<0在[0，10]上有6個零點11．已知函數(shù)SKIPIF1<0定義域為SKIPIF1<0，則下列說法正確的是（

）A．若SKIPIF1<0，則函數(shù)SKIPIF1<0圖象關(guān)于SKIPIF1<0對稱B．函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0對稱C．函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0對稱D．函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0對稱12．已知函數(shù)SKIPIF1<0，且SKIPIF1<0的對稱中心為SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則下列選項正確的是（

）A．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減 B．SKIPIF1<0的最小值是-1C．SKIPIF1<0在SKIPIF1<0上的函數(shù)值大于0 D．SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對稱三、填空題13．已知函數(shù)SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0的定義域均為R，若SKIPIF1<0，SKIPIF1<0都為偶函數(shù)，則SKIPIF1<0________．14．已知函數(shù)SKIPIF1<0，SKIPIF1<0的最大值為SKIPIF1<0，最小值為SKIPIF1<0，則SKIPIF1<0______.15．已知函數(shù)SKIPIF1<0與SKIPIF1<0的定義域均為SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0為偶函數(shù)，則SKIPIF1<0___________．16．已知定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，設(shè)函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖象交于點SKIPIF1<0（SKIPIF1<0為偶數(shù)），則SKIPIF1<0的值為__________．考點三奇偶性、周期性與對稱性一、單選題1．已知函數(shù)SKIPIF1<0的圖象關(guān)于原點對稱，且滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知函數(shù)SKIPIF1<0的圖像既關(guān)于直線SKIPIF1<0對稱，又關(guān)于點SKIPIF1<0對稱，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．03．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對稱，且關(guān)于點SKIPIF1<0中心對稱.設(shè)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．2020 B．2022 C．2024 D．20264．已知函數(shù)SKIPIF1<0對任意SKIPIF1<0都有SKIPIF1<0，且SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0.則下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱B．函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱C．當(dāng)SKIPIF1<0時，SKIPIF1<0D．函數(shù)SKIPIF1<0的最小正周期為25．已知定義在R上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0是偶函數(shù)，則（）A．SKIPIF1<0是偶函數(shù) B．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱C．SKIPIF1<0是奇函數(shù) D．SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱6．定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0為奇函數(shù).當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0（

）A．1 B．SKIPIF1<0 C．0 D．27．已知函數(shù)SKIPIF1<0的定義域為R，SKIPIF1<0為奇函數(shù)，且對于任意SKIPIF1<0，都有SKIPIF1<0，則下列結(jié)論中一定成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0為偶函數(shù) D．SKIPIF1<0為奇函數(shù)8．設(shè)函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0.若SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0為偶函數(shù) D．SKIPIF1<0的圖象關(guān)于SKIPIF1<0對稱二、多選題9．對于定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，下列說法正確的是（

）A．若SKIPIF1<0是奇函數(shù)，則SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱B．若對SKIPIF1<0，有SKIPIF1<0，則SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱C．若函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，則SKIPIF1<0為偶函數(shù)D．若SKIPIF1<0，則SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱10．設(shè)函數(shù)f（x）的定義域為R，且函數(shù)SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對稱，函數(shù)SKIPIF1<0的圖像關(guān)于點（3，0）對稱，則下列說法正確的是（

）A．4是f（x）的周期 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<011．已知SKIPIF1<0是定義在R上的偶函數(shù)，且對任意SKIPIF1<0，有SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則（

）A．SKIPIF1<0是以2為周期的周期函數(shù)B．點SKIPIF1<0是函數(shù)SKIPIF1<0的一個對稱中心C．SKIPIF1<0D．函數(shù)SKIPIF1<0有3個零點12．定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0圖像關(guān)于坐標(biāo)原點對稱，且SKIPIF1<0時，SKIPIF1<0，則下列說法正確的有（

）A．SKIPIF1<0 B．SKIPIF1<0的最小正周期為SKIPIF1<0C．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減 D．SKIPIF1<0時，SKIPIF1<013．已知函數(shù)SKIPIF1<0，SKIPIF1<0的定義域均為SKIPIF1<0，SKIPIF1<0是奇函數(shù)，且SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0為奇函數(shù) B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<014．設(shè)函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0.若SKIPIF1<0，則下列關(guān)于SKIPIF1<0的說法正確的有（

）A．SKIPIF1<0的一個周期為4 B．點SKIPIF1<0是函數(shù)的一個對稱中心C．SKIPIF1<0時，SKIPIF1<0 D．SKIPIF1<015．設(shè)定義在R上的函數(shù)SKIPIF1<0與SKIPIF1<0的導(dǎo)函數(shù)分別為SKIPIF1<0和SKIPIF1<0．若SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0為奇函數(shù)，則（

）．A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<016．設(shè)定義在R上的函數(shù)SKIPIF1<0與SKIPIF1<0的導(dǎo)數(shù)分別為SKIPIF1<0與SKIPIF1<0，已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，則下列結(jié)論一定成立的是（

）A．函數(shù)SKIPIF1<0