新高考數(shù)學(xué)一輪復(fù)習(xí)函數(shù)重難點(diǎn)專題08函數(shù)的周期性（原卷版）

專題08函數(shù)的周期性專項(xiàng)突破一周期函數(shù)的定義與求解1．有下面兩個(gè)命題：①若SKIPIF1<0是周期函數(shù)，則SKIPIF1<0是周期函數(shù)；②若SKIPIF1<0是周期函數(shù)，則SKIPIF1<0是周期函數(shù)，則下列說法中正確的是（

）．A．①②都正確 B．①正確②錯(cuò)誤 C．①錯(cuò)誤②正確 D．①②都錯(cuò)誤2．若函數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0可以是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知定義在SKIPIF1<0上的非常數(shù)函數(shù)SKIPIF1<0滿足：對于每一個(gè)實(shí)數(shù)SKIPIF1<0，都有SKIPIF1<0，則SKIPIF1<0的周期為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．若定義在R上的偶函數(shù)f(x)滿足SKIPIF1<0且SKIPIF1<0時(shí)，SKIPIF1<0，則方程SKIPIF1<0的解有（

）A．2個(gè) B．3個(gè)C．4個(gè) D．多于4個(gè)5．設(shè)SKIPIF1<0是定義在實(shí)數(shù)集SKIPIF1<0上的函數(shù)，且滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0是（

）A．偶函數(shù)，又是周期函數(shù) B．偶函數(shù)，但不是周期函數(shù)C．奇函數(shù)，又是周期函數(shù) D．奇函數(shù)，但不是周期函數(shù)6．已知函數(shù)SKIPIF1<0的最小正周期為3，則函數(shù)SKIPIF1<0的最小正周期為______．7．函數(shù)SKIPIF1<0為定義在SKIPIF1<0上的奇函數(shù)，且滿足SKIPIF1<0，則SKIPIF1<0的周期為__________．8．若定義在SKIPIF1<0上的非零函數(shù)SKIPIF1<0，對任意實(shí)數(shù)SKIPIF1<0，存在常數(shù)SKIPIF1<0，使得SKIPIF1<0恒成立，則稱SKIPIF1<0是一個(gè)“SKIPIF1<0函數(shù)”，試寫出一個(gè)“SKIPIF1<0函數(shù)”：__________．專項(xiàng)突破二利用周期性求函數(shù)值(或解析式)1．已知定義在R上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．12．已知函數(shù)SKIPIF1<0是SKIPIF1<0上的偶函數(shù)，若對于SKIPIF1<0，都有SKIPIF1<0.且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．23．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．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知函數(shù)SKIPIF1<0的圖象關(guān)于原點(diǎn)對稱，且SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0（

）A．-11 B．-8 C．SKIPIF1<0 D．SKIPIF1<05．已知定義在R上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0的值為（

）．A．SKIPIF1<0 B．0 C．1 D．26．已知函數(shù)SKIPIF1<0滿足：對任意SKIPIF1<0，SKIPIF1<0．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．定義在R上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．1 B．2 C．4 D．88．已知函數(shù)SKIPIF1<0的定義域?yàn)镽，且滿足SKIPIF1<0，當(dāng)SKIPIF1<0，SKIPIF1<0時(shí)，f(x)＝SKIPIF1<0，則f(7)SKIPIF1<0______.9．已知SKIPIF1<0是以SKIPIF1<0為周期的偶函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0________．10．已知SKIPIF1<0是定義在SKIPIF1<0上的周期為3的奇函數(shù)，且SKIPIF1<0，則SKIPIF1<0___________.11．設(shè)定義在R上的函數(shù)SKIPIF1<0同時(shí)滿足以下條件：①SKIPIF1<0；②SKIPIF1<0；③當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0________.12．已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且函數(shù)SKIPIF1<0為偶函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0______．13．設(shè)SKIPIF1<0是定義在SKIPIF1<0上周期為4的偶函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則函數(shù)SKIPIF1<0在SKIPIF1<0上的解析式為__________.14．定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0__________.15．設(shè)f(x)是定義在R上的奇函數(shù)，且對任意實(shí)數(shù)x，恒有f(x＋2)＝－f(x)．當(dāng)x∈[0，2]時(shí)，f(x)＝2x－x2．（1）求證：f(x)是周期函數(shù)；（2）當(dāng)x∈[2，4]時(shí)，求f(x)的解析式；（3）計(jì)算f(0)＋f（1）＋f（2）＋…＋f(2019)．16．已知函數(shù)SKIPIF1<0是實(shí)數(shù)集SKIPIF1<0上的函數(shù)，且SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.(1)求SKIPIF1<0的周期.(2)求SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0的表達(dá)式.(3)若關(guān)于SKIPIF1<0的方程SKIPIF1<0在區(qū)間SKIPIF1<0上恰有4個(gè)解，求實(shí)數(shù)SKIPIF1<0的取值范圍.專項(xiàng)突破三抽象函數(shù)周期性1．定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，則下列是周期函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．已知函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，函數(shù)SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0對稱，則下列說法正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0的周期為2 D．SKIPIF1<03．已知SKIPIF1<0是奇函數(shù)，則下列等式成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0恒成立，若SKIPIF1<0，則SKIPIF1<0的值為（

）A．6 B．4 C．2 D．05．若定義在實(shí)數(shù)集R上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，對任意的SKIPIF1<0恒成立，則SKIPIF1<0（

）A．4 B．3 C．2 D．16．定義在正整數(shù)上的函數(shù)滿足SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．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(guān)于原點(diǎn)對稱，SKIPIF1<0，則SKIPIF1<0（

）A．1 B．2 C．3 D．48．已知SKIPIF1<0是定義域?yàn)镽的偶函數(shù)，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0.若SKIPIF1<0是偶函數(shù)，則SKIPIF1<0（

）A．－3 B．－2 C．2 D．39．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，滿足SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，SKIPIF1<0為偶函數(shù)，SKIPIF1<0為奇函數(shù)，則下列等式不一定成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，SKIPIF1<0為偶函數(shù)，SKIPIF1<0為奇函數(shù)，則SKIPIF1<0=（

）A．SKIPIF1<0 B．0 C．1 D．212．已知函數(shù)SKIPIF1<0對SKIPIF1<0滿足：SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．413．已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，且SKIPIF1<0是偶函數(shù)，SKIPIF1<0是奇函數(shù)，則下列命題正確的個(gè)數(shù)是（

）①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0；④SKIPIF1<0.A．1 B．2 C．3 D．414．函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，且SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0為偶函數(shù) D．SKIPIF1<0為奇函數(shù)15．已知SKIPIF1<0是SKIPIF1<0上的奇函數(shù)，SKIPIF1<0是SKIPIF1<0上的偶函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0最小正周期為4 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<016．已知定義在R上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0對稱，則SKIPIF1<0___________.17．定義在實(shí)數(shù)集SKIPIF1<0上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0____________.18．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，對任意SKIPIF1<0，都有SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0的值為_________19．已知y=f(x)滿足對一切x，ySKIPIF1<0R都有f(x+2y)=f(x)+2f(y).(1)判斷y=f(x)的奇偶性并證明;(2)若f(1)=2，求f(-13)+f(-3)+f(22)+f(53)的值.20．已知f(x)是定義在R上的函數(shù)，滿足SKIPIF1<0．（1）若SKIPIF1<0，求SKIPIF1<0；（2）證明：函數(shù)f(x)的周期是2；（3）當(dāng)SKIPIF1<0時(shí)，f(x)＝2x，求f(x)在SKIPIF1<0時(shí)的解析式，并寫出f(x)在SKIPIF1<0時(shí)的解析式．專項(xiàng)突破四函數(shù)周期性的應(yīng)用1．已知在R上的函數(shù)SKIPIF1<0滿足對于任意實(shí)數(shù)SKIPIF1<0都有SKIPIF1<0，SKIPIF1<0，且在區(qū)間SKIPIF1<0上只有SKIPIF1<0和SKIPIF1<0兩個(gè)零點(diǎn)，則SKIPIF1<0在區(qū)間SKIPIF1<0上根的個(gè)數(shù)為（）A．404 B．405 C．406 D．2032．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的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．已知函數(shù)SKIPIF1<0是定義在R上的偶函數(shù)，且SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0在區(qū)間SKIPIF1<0上零點(diǎn)的個(gè)數(shù)為（

）A．2 B．3 C．4 D．54．已知函數(shù)f（x）是定義在R上的偶函數(shù)，滿足f（x＋2）＝f（﹣x），當(dāng)x∈[0，1]時(shí)SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)是（

）A．5 B．6 C．7 D．85．辛亥革命發(fā)生在辛亥年，戊戌變法發(fā)生在戊戌年.辛亥年、戊戌年這些都是我國古代的一種紀(jì)年方法.甲、乙、丙、丁、戊、己、庚、辛、壬、癸十個(gè)符號(hào)叫天干；子、丑、寅、卯、辰、巳、午、未、申、酉、戌、亥十二個(gè)符號(hào)叫地支.按天干地支順序相組配用來紀(jì)年叫干支紀(jì)年法.例如：天干中“甲”和地支中“子”相配即為“甲子年”，天干中“乙”和地支中“丑”相配即為“乙丑年”，以此紀(jì)年法恰好六十年一循環(huán).那么下列干支紀(jì)年法紀(jì)年錯(cuò)誤項(xiàng)是（

）A．庚子年 B．丙卯年 C．癸亥年 D．戊申年6．已知定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0，SKIPIF1<0，則下面結(jié)論正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．定義在R上的函數(shù)SKIPIF1<0滿足以下三個(gè)條件：①對于任意的實(shí)數(shù)SKIPIF1<0，都有SKIPIF1<0成立；②函數(shù)SKIPIF1<0的圖象關(guān)于y軸對稱；③對任意的SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0成立.則SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．已知f（x）是定義在R上周期為2的偶函數(shù)，若當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則函數(shù)SKIPIF1<0在區(qū)間SKIP