新高考一輪復(fù)習(xí)核心考點講與練考點03 函數(shù)及其性質(zhì)原卷版

考點03函數(shù)及其性質(zhì)（核心考點講與練）1.函數(shù)的概念設(shè)A，B是兩個非空數(shù)集，如果按照確定的法則f，對A中的任意數(shù)x，都有唯一確定的數(shù)y與它對應(yīng)，那么就稱f：A→B為從集合A到集合B的一個函數(shù)，記作y＝f(x)，x∈A.2.函數(shù)的定義域、值域(1)函數(shù)y＝f(x)自變量取值的范圍(數(shù)集A)叫做這個函數(shù)的定義域；所有函數(shù)值構(gòu)成的集合{y|y＝f(x)，x∈A}叫做這個函數(shù)的值域.(2)如果兩個函數(shù)的定義域相同，并且對應(yīng)法則完全一致，則這兩個函數(shù)為相等函數(shù).3.函數(shù)的表示法表示函數(shù)的常用方法有解析法、圖象法和列表法.4.分段函數(shù)(1)在函數(shù)的定義域內(nèi)，對于自變量x的不同取值區(qū)間，有著不同的對應(yīng)法則，這種函數(shù)稱為分段函數(shù).(2)分段函數(shù)是一個函數(shù)，分段函數(shù)的定義域是各段定義域的并集，值域是各段值域的并集.5.函數(shù)的單調(diào)性(1)單調(diào)函數(shù)的定義增函數(shù)減函數(shù)定義設(shè)函數(shù)y＝f(x)的定義域為A，區(qū)間M?A，如果取區(qū)間M中任意兩個值x1，x2，改變量Δx＝x2－x1>0，則當(dāng)Δy＝f(x2)－f(x1)>0時，就稱函數(shù)y＝f(x)在區(qū)間M上是增函數(shù)Δy＝f(x2)－f(x1)<0時，就稱函數(shù)y＝f(x)在區(qū)間M上是減函數(shù)圖象描述自左向右看圖象是上升的自左向右看圖象是下降的(2)如果一個函數(shù)在某個區(qū)間M上是增函數(shù)或是減函數(shù)，就說這個函數(shù)在這個區(qū)間M上具有單調(diào)性，區(qū)間M稱為單調(diào)區(qū)間.6.函數(shù)的最值前提設(shè)函數(shù)y＝f(x)的定義域為I，如果存在實數(shù)M滿足條件(1)對于任意x∈I，都有f(x)≤M；(2)存在x0∈I，使得f(x0)＝M(3)對于任意x∈I，都有f(x)≥M；(4)存在x0∈I，使得f(x0)＝M結(jié)論M為最大值M為最小值7.函數(shù)的奇偶性奇偶性定義圖象特點奇函數(shù)設(shè)函數(shù)y＝f(x)的定義域為D，如果對D內(nèi)的任意一個x，都有－x∈D，且f(－x)＝－f(x)，則這個函數(shù)叫做奇函數(shù)關(guān)于原點對稱偶函數(shù)設(shè)函數(shù)y＝g(x)的定義域為D，如果對D內(nèi)的任意一個x，都有－x∈D，且g(－x)＝g(x)，則這個函數(shù)叫做偶函數(shù)關(guān)于y軸對稱8.函數(shù)的周期性(1)周期函數(shù)：對于函數(shù)y＝f(x)，如果存在一個非零常數(shù)T，使得當(dāng)x取定義域內(nèi)的任何值時，都有f(x＋T)＝f(x)，那么就稱函數(shù)y＝f(x)為周期函數(shù)，稱T為這個函數(shù)的周期.(2)最小正周期：如果在周期函數(shù)f(x)的所有周期中存在一個最小的正數(shù)，那么這個最小正數(shù)就叫做f(x)的最小正周期.1.利用基本不等式求最值時，要注意其必須滿足的三個條件：（1）“一正”就是各項必須為正數(shù)；（2）“二定”就是要求和的最小值，必須把構(gòu)成和的二項之積轉(zhuǎn)化成定值；要求積的最大值，則必須把構(gòu)成積的因式的和轉(zhuǎn)化成定值；（3）“三相等”是利用基本不等式求最值時，必須驗證等號成立的條件，若不能取等號則這個定值就不是所求的最值，這也是最容易發(fā)生錯誤的地方.2.已知函數(shù)零點(方程根)的個數(shù)求參數(shù)值(取值范圍)常用的方法：（1）直接法：直接求解方程得到方程的根，再通過解不等式確定參數(shù)范圍；（2）分離參數(shù)法：先將參數(shù)分離，轉(zhuǎn)化成求函數(shù)的值域問題加以解決；（3）數(shù)形結(jié)合法：先對解析式變形，進(jìn)而構(gòu)造兩個函數(shù)，然后在同一平面直角坐標(biāo)系中畫出函數(shù)的圖象，利用數(shù)形結(jié)合的方法求解.3.函數(shù)的對稱性與單調(diào)性，指數(shù)式、對數(shù)式的大小比較．比較指數(shù)式大小時，常?；癁橥讛?shù)的冪，利用指數(shù)函數(shù)性質(zhì)比較，或化為同指數(shù)的冪，利用冪函數(shù)性質(zhì)比較，比較對數(shù)式大小，常?；癁橥讛?shù)的對數(shù)，利用對數(shù)函數(shù)性質(zhì)比較，如果不能化為同底數(shù)或同指數(shù)，或不同類型的數(shù)常常借助中間值如0或1比較大?。?.導(dǎo)數(shù)是研究函數(shù)的單調(diào)性、極值(最值)最有效的工具，而函數(shù)是高中數(shù)學(xué)中重要的知識點，對導(dǎo)數(shù)的應(yīng)用的考查主要從以下幾個角度進(jìn)行：（1）考查導(dǎo)數(shù)的幾何意義，往往與解析幾何、微積分相聯(lián)系．（2）利用導(dǎo)數(shù)求函數(shù)的單調(diào)區(qū)間，判斷單調(diào)性；已知單調(diào)性，求參數(shù)．（3）利用導(dǎo)數(shù)求函數(shù)的最值(極值)，解決生活中的優(yōu)化問題．（4）考查數(shù)形結(jié)合思想的應(yīng)用．函數(shù)及其表示一、單選題1．（2022·天津市第四十七中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0，若在區(qū)間SKIPIF1<0上存在SKIPIF1<0個不同的數(shù)SKIPIF1<0，使得SKIPIF1<0成立，則SKIPIF1<0的取值集合是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·天津市第四十七中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·河北·模擬預(yù)測）設(shè)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<04．（2022·浙江嘉興·二模）已知函數(shù)SKIPIF1<0的圖象如圖所示，則SKIPIF1<0的解析式可能是（

）（SKIPIF1<0是自然對數(shù)的底數(shù)）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·天津·耀華中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0（SKIPIF1<0，且SKIPIF1<0）在區(qū)間SKIPIF1<0上為單調(diào)函數(shù)，若函數(shù)SKIPIF1<0有三個不同的零點，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·浙江省義烏中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0，則圖象為下圖的函數(shù)可能是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2021·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0的定義域是SKIPIF1<0（m，n為整數(shù)），值域是SKIPIF1<0，則滿足條件的整數(shù)對SKIPIF1<0的個數(shù)是（

）A．2 B．3 C．4 D．58．（2020·南開中學(xué)模擬預(yù)測）下列各組函數(shù)中，表示同一函數(shù)的是（

）A．SKIPIF1<0與SKIPIF1<0 B．SKIPIF1<0與SKIPIF1<0C．SKIPIF1<0與SKIPIF1<0 D．SKIPIF1<0與SKIPIF1<09．（2020·廣東中山·模擬預(yù)測）下列各組表示同一函數(shù)的是（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<010.（2020·全國·一模）網(wǎng)購女鞋時，常常會看到一張女鞋尺碼對照表如下，第一行是我們習(xí)慣稱呼的“鞋號”（單位：.號），第二行是腳長（單位：SKIPIF1<0），請根據(jù)表中數(shù)據(jù)，思考：他們家正好有一款“32號”的女鞋在搞打折，那么適合購買這款鞋的腳長的取值范圍是（

）鞋碼3536373839腳長225230235240245A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題11．（2022·江蘇南通·模擬預(yù)測）已知定義在R上的函數(shù)SKIPIF1<0的圖象連續(xù)不間斷，當(dāng)SKIPIF1<0時，SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減C．若SKIPIF1<0，則SKIPIF1<0D．若SKIPIF1<0是SKIPIF1<0的兩個零點，且SKIPIF1<0，則SKIPIF1<012．（2022·江蘇·沭陽如東中學(xué)模擬預(yù)測）華人數(shù)學(xué)家李天巖和美國數(shù)學(xué)家約克給出了“混沌”的數(shù)學(xué)定義，由此發(fā)展的混沌理論在生物學(xué)?經(jīng)濟(jì)學(xué)和社會學(xué)領(lǐng)域都有重要作用.在混沌理論中，函數(shù)的周期點是一個關(guān)鍵概念，定義如下：設(shè)SKIPIF1<0是定義在R上的函數(shù)，對于SKIPIF1<0R，令SKIPIF1<0，若存在正整數(shù)k使得SKIPIF1<0，且當(dāng)0<j<k時，SKIPIF1<0，則稱SKIPIF1<0是SKIPIF1<0的一個周期為k的周期點.若SKIPIF1<0，下列各值是SKIPIF1<0周期為2的周期點的有（

）A．0 B．SKIPIF1<0 C．SKIPIF1<0 D．113．（2022·江蘇江蘇·一模）下列函數(shù)中，最大值是1的函數(shù)有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<014．（2021·江西·模擬預(yù)測）已知函數(shù)SKIPIF1<0，則下列敘述正確的是（

）A．SKIPIF1<0的值域為SKIPIF1<0 B．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增C．SKIPIF1<0 D．若SKIPIF1<0，則SKIPIF1<0的最小值為-315．（2021·江西·模擬預(yù)測）下列各組函數(shù)中表示同一個函數(shù)的是（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<016．（2021·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0，則SKIPIF1<0和SKIPIF1<0滿足（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空題17．（2022·福建·三模）寫出一個同時具有下列性質(zhì)①②③的函數(shù)SKIPIF1<0________.①定義域為SKIPIF1<0；②值域為SKIPIF1<0；③對任意SKIPIF1<0且SKIPIF1<0，均有SKIPIF1<0.18．（2022·山東淄博·一模）以模型SKIPIF1<0去擬合一組數(shù)據(jù)時，設(shè)SKIPIF1<0，將其變換后得到線性回歸方程SKIPIF1<0，則SKIPIF1<0______．19．（2022·全國·模擬預(yù)測）已知SKIPIF1<0，則SKIPIF1<0______．20．（2022·重慶·模擬預(yù)測）已知定義在R上的函數(shù)SKIPIF1<0不是常值函數(shù)，且同時滿足：①SKIPIF1<0；②對任意SKIPIF1<0，均存在SKIPIF1<0使得SKIPIF1<0成立；則函數(shù)SKIPIF1<0______．（寫出一個符合條件的答案即可）四、雙空題21．（2022·浙江嘉興·二模）已知函數(shù)SKIPIF1<0的定義域為R，且滿足SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0若SKIPIF1<0，則實數(shù)SKIPIF1<0___________，SKIPIF1<0___________.22．（2022·江蘇·金陵中學(xué)二模）已知函數(shù)SKIPIF1<0，則SKIPIF1<0的最小正周期為___________；當(dāng)SKIPIF1<0時，SKIPIF1<0的值域為___________.23．（2022·山東濟(jì)南·一模）已知函數(shù)SKIPIF1<0，對任意非零實數(shù)x，均滿足SKIPIF1<0.則SKIPIF1<0的值為___________；函數(shù)SKIPIF1<0的最小值為___________.函數(shù)的基本性質(zhì)一、函數(shù)的單調(diào)性一、單選題1．（2022·天津·耀華中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0，則下述關(guān)系式正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·廣東廣州·二模）下列函數(shù)中，既是偶函數(shù)又在SKIPIF1<0上單調(diào)遞增的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·遼寧撫順·一模）已知函數(shù)SKIPIF1<0對任意SKIPIF1<0都有SKIPIF1<0，若SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，且對任意的，SKIPIF1<0，當(dāng)SKIPIF1<0時，都有SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國·哈師大附中模擬預(yù)測（理））已知實數(shù)SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題5．（2022·廣東茂名·二模）若對任意的SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0，則m的值可能是（

）（注SKIPIF1<0…為自然對數(shù)的底數(shù)）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．16．（2022·福建泉州·模擬預(yù)測）已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，且滿足SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，SKIPIF1<0為非零常數(shù)，則下列說法正確的是（

）A．當(dāng)SKIPIF1<0時，SKIPIF1<0B．當(dāng)SKIPIF1<0時，SKIPIF1<0在SKIPIF1<0單調(diào)遞增C．當(dāng)SKIPIF1<0時，SKIPIF1<0在SKIPIF1<0的值域為SKIPIF1<0D．當(dāng)SKIPIF1<0，且SKIPIF1<0時，若將函數(shù)SKIPIF1<0與SKIPIF1<0的圖象在SKIPIF1<0的SKIPIF1<0個交點記為SKIPIF1<0，則SKIPIF1<07．（2022·廣東廣東·一模）下列四個函數(shù)中，以SKIPIF1<0為周期且在SKIPIF1<0上單調(diào)遞增的偶函數(shù)有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空題8．（2022·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0，若對任意的正數(shù)SKIPIF1<0，滿足SKIPIF1<0SKIPIF1<0，則SKIPIF1<0的最小值為_________.9．（2022·山東·濟(jì)南市歷城第二中學(xué)模擬預(yù)測）函數(shù)SKIPIF1<0在SKIPIF1<0上是減函數(shù)，則實數(shù)SKIPIF1<0的范圍是_______.10．（2022·北京豐臺·一模）設(shè)函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，能說明“若函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值為SKIPIF1<0，則函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增“為假命題的一個函數(shù)是__________.四、解答題11．（2022·江蘇江蘇·一模）已知實數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0，SKIPIF1<0是自然對數(shù)的底數(shù).(1)當(dāng)SKIPIF1<0時，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)求證：SKIPIF1<0存在極值點SKIPIF1<0，并求SKIPIF1<0的最小值.12．（2022·山東青島·一模）已知函數(shù)SKIPIF1<0．(1)若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，求實數(shù)SKIPIF1<0的取值范圍；(2)設(shè)函數(shù)SKIPIF1<0，若SKIPIF1<0，求SKIPIF1<0的值．13．（2022·湖北·黃岡中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0(1)若SKIPIF1<0，且SKIPIF1<0，試比較SKIPIF1<0與SKIPIF1<0的大小關(guān)系，并說明理由；(2)若SKIPIF1<0，且SKIPIF1<0，證明：（i）SKIPIF1<0；（ii）SKIPIF1<0.（參考數(shù)據(jù)：SKIPIF1<0）二、函數(shù)的最值一、單選題1．（2021·湖南·模擬預(yù)測）已知奇函數(shù)SKIPIF1<0為SKIPIF1<0上的增函數(shù)，且在區(qū)間SKIPIF1<0上的最大值為9，最小值為-6，則SKIPIF1<0的值為（

）A．3 B．1 C．-1 D．-32．（2022·浙江嘉興·二模）設(shè)a，SKIPIF1<0，若SKIPIF1<0時，恒有SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·浙江省義烏中學(xué)模擬預(yù)測）設(shè)SKIPIF1<0，則有（

）A．存在SKIPIF1<0成立 B．任意SKIPIF1<0恒成立C．任意SKIPIF1<0恒成立 D．存在SKIPIF1<0成立4．（2022·重慶·二模）已知SKIPIF1<0，若SKIPIF1<0對任意SKIPIF1<0恒成立，則實數(shù)m的最大值為（

）A．2 B．4 C．SKIPIF1<0 D．SKIPIF1<05．（2022·天津?qū)嶒炛袑W(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0，若?SKIPIF1<0∈R，使得SKIPIF1<0成立，則實數(shù)m的取值范圍為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題6．（2022·湖北·一模）已知函數(shù)SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0是偶函數(shù) B．SKIPIF1<0在（0，+∞）上單調(diào)遞減C．SKIPIF1<0是周期函數(shù) D．SKIPIF1<0≥-1恒成立7．（2022·福建漳州·一模）已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0的定義域為SKIPIF1<0 B．SKIPIF1<0是偶函數(shù)C．函數(shù)SKIPIF1<0的零點為0 D．當(dāng)SKIPIF1<0時，SKIPIF1<0的最大值為SKIPIF1<0三、填空題8．（2022·浙江省諸暨市第二高級中學(xué)模擬預(yù)測）已知平面單位向量SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0.設(shè)SKIPIF1<0，SKIPIF1<0，向量SKIPIF1<0，SKIPIF1<0的夾角為SKIPIF1<0，則SKIPIF1<0的最大值是_______________.9．（2022·湖北·一模）已知函數(shù)SKIPIF1<0（x>0），若SKIPIF1<0的最大值為SKIPIF1<0，則正實數(shù)a=___________.10．（2020·山東臨沂·二模）若SKIPIF1<0，SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍為___________.11．（2021·北京延慶·模擬預(yù)測）同學(xué)們，你們是否注意到：自然下垂的鐵鏈；空曠的田野上，兩根電線桿之間的電線；峽谷的上空，橫跨深澗的觀光索道的鋼索．這些現(xiàn)象中都有相似的曲線形態(tài)．事實上，這些曲線在數(shù)學(xué)上常常被稱為懸鏈線．懸鏈線的相關(guān)理論在工程、航海、光學(xué)等方面有廣泛的應(yīng)用．在恰當(dāng)?shù)淖鴺?biāo)系中，這類函數(shù)的表達(dá)式可以為SKIPIF1<0（其中SKIPIF1<0，SKIPIF1<0是非零常數(shù)，無理數(shù)SKIPIF1<0…），對于函數(shù)SKIPIF1<0以下結(jié)論正確的是______．①如果SKIPIF1<0，那么函數(shù)SKIPIF1<0為奇函數(shù)；②如果SKIPIF1<0，那么SKIPIF1<0為單調(diào)函數(shù)；③如果SKIPIF1<0，那么函數(shù)SKIPIF1<0沒有零點；④如果SKIPIF1<0那么函數(shù)SKIPIF1<0的最小值為2．12．（2021·浙江浙江·二模）設(shè)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，且SKIPIF1<0的最大值是SKIPIF1<0，則SKIPIF1<0___________.四、解答題13．（2022·海南·模擬預(yù)測）已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0在區(qū)間-π2,0上的最大值和最小值；(2)設(shè)SKIPIF1<0，若當(dāng)SKIPIF1<0時，SKIPIF1<0，求實數(shù)a的取值范圍.14．（2021·江西·模擬預(yù)測）設(shè)函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且當(dāng)SKIPIF1<0時，SKIPIF1<0.(1)求SKIPIF1<0的解析式；(2)若SKIPIF1<0，使得SKIPIF1<0，求實數(shù)SKIPIF1<0的取值范圍.三、函數(shù)的奇偶性一、單選題1．（2022·廣東茂名·二模）已知SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·湖南湘潭·三模）函數(shù)SKIPIF1<0的部分圖象大致為（

）A． B．C． D．3．（2022·廣東茂名·二模）已知函數(shù)SKIPIF1<0，SKIPIF1<0分別是定義在R上的偶函數(shù)和奇函數(shù)，且SKIPIF1<0，若函數(shù)SKIPIF1<0有唯一零點，則正實數(shù)SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．24．（2021·全國·模擬預(yù)測）已知SKIPIF1<0為定義在R上的奇函數(shù)，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0（

）A．﹣2022 B．2022 C．SKIPIF1<0 D．SKIPIF1<05．（2022·遼寧·大連二十四中模擬預(yù)測）已知函數(shù)SKIPIF1<0，若SKIPIF1<0且SKIPIF1<0，則有（

）A．SKIPIF1<0可能是奇函數(shù)，也可能是偶函數(shù) B．SKIPIF1<0C．SKIPIF1<0時，SKIPIF1<0 D．SKIPIF1<06．（2022·江蘇南通·模擬預(yù)測）若函數(shù)SKIPIF1<0為奇函數(shù)，則實數(shù)SKIPIF1<0的值為（

）A．1 B．2 C．SKIPIF1<0 D．SKIPIF1<07．（2022·湖北·二模）已知函數(shù)SKIPIF1<0，則使不等式SKIPIF1<0成立的x的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2022·天津三中二模）設(shè)函數(shù)SKIPIF1<0的定義域為D，若對任意的SKIPIF1<0，且SKIPIF1<0，恒有SKIPIF1<0，則稱函數(shù)SKIPIF1<0具有對稱性，其中點SKIPIF1<0為函數(shù)SKIPIF1<0的對稱中心，研究函數(shù)SKIPIF1<0的對稱中心，求SKIPIF1<0（

）A．2022 B．4043 C．4044 D．8086二、多選題9．（2022·江蘇泰州·模擬預(yù)測）已知定義在SKIPIF1<0上的單調(diào)遞增的函數(shù)SKIPIF1<0滿足：任意SKIPIF1<0，有SKIPIF1<0，SKIPIF1<0，則（

）A．當(dāng)SKIPIF1<0時，SKIPIF1<0B．任意SKIPIF1<0，SKIPIF1<0C．存在非零實數(shù)SKIPIF1<0，使得任意SKIPIF1<0，SKIPIF1<0D．存在非零實數(shù)SKIPIF1<0，使得任意SKIPIF1<0，SKIPIF1<0三、填空題10．（2022·廣東深圳·二模）已知函數(shù)SKIPIF1<0是偶函數(shù)，則SKIPIF1<0___________．11．（2022·山東菏澤·一模）已知奇函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是增函數(shù)，且SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0，SKIPIF1<0時，都有SKIPIF1<0，則不等式SKIPIF1<0的解集為______．四、函數(shù)的周期性一、單選題1．（2022·山東濟(jì)寧·一模）定義在R上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0（

）A．0 B．1 C．－1 D．20222．（2022·福建·模擬預(yù)測）已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．1 B．0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·江蘇江蘇·二模）已知SKIPIF1<0是定義域為R的偶函數(shù)，f(5.5)＝2，g(x)＝(x－1)SKIPIF1<0.若g(x＋1)是偶函數(shù)，則SKIPIF1<0＝(

)A．－3 B．－2 C．2 D．3二、多選題4．（2022·河北·模擬預(yù)測）若函數(shù)SKIPIF1<0（SKIPIF1<0）是周期為2的奇函數(shù)．則下列選項一定正確的是（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱B．2是函數(shù)SKIPIF1<0的一個周期C．SKIPIF1<0D．SKIPIF1<05．（2022·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0是函數(shù)SKIPIF1<0的一個周期B．SKIPIF1<0是函數(shù)SKIPIF1<0的一條對稱軸C．函數(shù)SKIPIF1<0的最大值為SKIPIF1<0，最小值為SKIPIF1<0D．函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增6．（2021·廣東肇慶·模擬預(yù)測）已知定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0對任意的SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，函數(shù)SKIPIF1<0且SKIPIF1<0，則下列結(jié)論正確的有（

）A．SKIPIF1<0是周期為SKIPIF1<0的周期函數(shù)B．當(dāng)SKIPIF1<0時，SKIPIF1<0C．若SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則SKIPIF1<0D．若方程SKIPIF1<0在SKIPIF1<0上有SKIPIF1<0個不同的實數(shù)根，則實數(shù)SKIPIF1<0的取值范圍是SKIPIF1<0三、填空題7．（2022·廣東茂名·二模）請寫出一個函數(shù)SKIPIF1<0_______，使之同時具有以下性質(zhì)：①圖象關(guān)于y軸對稱；②SKIPIF1<0，SKIPIF1<0．8．（2022·重慶·二模）已知定義域為R的函數(shù)SKIPIF1<0滿足SKIPIF1<0且SKIPIF1<0，則函數(shù)SKIPIF1<0的解析式可以是______.五、函數(shù)的對稱性一、單選題1．（2022·廣東佛山·模擬預(yù)測）已知函數(shù)SKIPIF1<0的圖象與函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，將SKIPIF1<0的圖象向右平移SKIPIF1<0個單位長度后得到函數(shù)SKIPIF1<0的圖象，則函數(shù)SKIPIF1<0在SKIPIF1<0時的值域為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2021·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0，且對任意的實數(shù)x，SKIPIF1<0恒成立.若存在實數(shù)SKIPIF1<0，SKIPIF1<0，…，SKIPIF1<0（SKIPIF1<0），使得SKIPIF1<0成立，則n的最大值為（

）A．25 B．26 C．28 D．313．（2021·浙江·模擬預(yù)測）已知定義在SKIPIF1<0上的圖象連續(xù)的函數(shù)SKIPIF1<0的導(dǎo)數(shù)是SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2021·廣東·梅州市梅江區(qū)嘉應(yīng)中學(xué)模擬預(yù)測）已知定義在R上的函數(shù)SKIPIF1<0滿足：對任意SKIPIF1<0，都有SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0（其中SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)）．設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則a，b，c的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題5．（2022·江蘇·新沂市第一中學(xué)模擬預(yù)測）已知三次函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0的圖象關(guān)于點（1，0）對稱，且SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0有3個零點C．SKIPIF1<0的對稱中心是SKIPIF1<0 D．SKIPIF1<0三、填空題6．（2022·重慶·模擬預(yù)測）寫出一個同時滿足下列三個條件的函數(shù)SKIPIF1<0的解析式__________.①SKIPIF1<0的定義域為SKIPIF1<0，值域為SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0在SKIPIF1<0上單調(diào)遞減.7．（2022·廣東廣州·二模）函數(shù)SKIPIF1<0的所有零點之和為__________．一、單選題1．（2020·山東·高考真題）已知函數(shù)SKIPIF1<0是偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0，則該函數(shù)在SKIPIF1<0上的圖像大致是（

）A． B．C． D．2．（2020·山東·高考真題）已知函數(shù)SKIPIF1<0的定義域是SKIPIF1<0，若對于任意兩個不相等的實數(shù)SKIPIF1<0，SKIPIF1<0，總有SKIPIF1<0成立，則函數(shù)SKIPIF1<0一定是（

）A．奇函數(shù) B．偶函數(shù) C．增函數(shù) D．減函數(shù)3．（2020·山東·高考真題）函數(shù)SKIPIF1<0的定義域是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2021·全國·高考真題（理））設(shè)函數(shù)SKIPIF1<0的定義域為R，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SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2021·全國·高考真題（文））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<06．（2021·全國·高考真題（理））設(shè)函數(shù)SKIPIF1<0，則下列函數(shù)中為奇函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題7．（2021·全國·高考真題）已知函數(shù)SKIPIF1<0是偶函數(shù)，則SKIPIF1<0______.三、解答題8．（2021·全國·高考真題（文））已知函數(shù)SKIPIF1<0．（1）畫出SKIPIF1<0和SKIPIF1<0的圖像；（2）若SKIPIF1<0，求a的取值范圍．一、單選題1.（2022·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0的值域為SKIPIF1<0，則a的最小值為（）A.1 B.2 C.3 D.42.（2022·北京·北師大實驗中學(xué)模擬預(yù)測）下列函數(shù)中，既是偶函數(shù)又在SKIPIF1<0單調(diào)遞增的函數(shù)是（）A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.（2022·全國·模擬預(yù)測）函數(shù)SKIPIF1<0在SKIPIF1<0上的大致圖象為（）A. B.C. D.4.（2022·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0，則SKIPIF1<0（）A.e B.1 C.SKIPIF1<0 D.SKIPIF1<05.（2022·全國·模擬預(yù)測）函數(shù)SKIPIF1<0的圖象大致為（）A. B.C. D.6.（2022·全國·模擬預(yù)測）已知定義域為R的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則不等式SKIPIF1<0的解集為（）A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.（2022·全國·模擬預(yù)測）若函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值與最小值之和不小于SKIPIF1<0，則實數(shù)a的取值范圍為（）A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.（2022·全國·模擬預(yù)測）已知SKIPIF1<0為R上的奇函數(shù)，SKIPIF1<0，若SKIPIF1<0且SKIPIF1<0，都有SKIPIF1<0，則不等式SKIPIF1<0的解集為（）A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<09.（2022·廣東汕頭·一模）定義在R上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，若關(guān)于x的方程SKIPIF1<0至少有8個實數(shù)解，則實數(shù)m的取值范圍是（）A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0