新高考數(shù)學(xué)二輪復(fù)習(xí)核心考點(diǎn)講與練重難點(diǎn)01七種零點(diǎn)問題原卷版

重難點(diǎn)01七種零點(diǎn)問題（核心考點(diǎn)講與練）方法技巧方法技巧1.轉(zhuǎn)化思想在函數(shù)零點(diǎn)問題中的應(yīng)用方程解的個數(shù)問題可轉(zhuǎn)化為兩個函數(shù)圖象交點(diǎn)的個數(shù)問題；已知方程有解求參數(shù)范圍問題可轉(zhuǎn)化為函數(shù)值域問題.2.判斷函數(shù)零點(diǎn)個數(shù)的常用方法(1)通過解方程來判斷.(2)根據(jù)零點(diǎn)存在性定理，結(jié)合函數(shù)性質(zhì)來判斷.(3)將函數(shù)y＝f(x)－g(x)的零點(diǎn)個數(shù)轉(zhuǎn)化為函數(shù)y＝f(x)與y＝g(x)圖象公共點(diǎn)的個數(shù)來判斷.3.正弦型函數(shù)的零點(diǎn)個數(shù)問題，可先求出零點(diǎn)的一般形式，再根據(jù)零點(diǎn)的分布得到關(guān)于整數(shù)SKIPIF1<0的不等式組，從而可求相應(yīng)的參數(shù)的取值范圍.4.涉及含參的函數(shù)零點(diǎn)問題，利用導(dǎo)數(shù)分類討論，研究函數(shù)的單調(diào)性、最值等，結(jié)合零點(diǎn)存在性定理，借助數(shù)形結(jié)合思想分析解決問題.5.函數(shù)零點(diǎn)的求解與判斷方法：（1）直接求零點(diǎn)：令f(x)＝0，如果能求出解，則有幾個解就有幾個零點(diǎn)．（2）零點(diǎn)存在性定理：利用定理不僅要函數(shù)在區(qū)間[a，b]上是連續(xù)不斷的曲線，且f(a)·f(b)＜0，還必須結(jié)合函數(shù)的圖象與性質(zhì)(如單調(diào)性、奇偶性)才能確定函數(shù)有多少個零點(diǎn)．（3）利用圖象交點(diǎn)的個數(shù)：將函數(shù)變形為兩個函數(shù)的差，畫兩個函數(shù)的圖象，看其交點(diǎn)的橫坐標(biāo)有幾個不同的值，就有幾個不同的零點(diǎn)．6.對于復(fù)合函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)問題，求解思路如下：（1）確定內(nèi)層函數(shù)SKIPIF1<0和外層函數(shù)SKIPIF1<0；（2）確定外層函數(shù)SKIPIF1<0的零點(diǎn)SKIPIF1<0；（3）確定直線SKIPIF1<0與內(nèi)層函數(shù)SKIPIF1<0圖象的交點(diǎn)個數(shù)分別為SKIPIF1<0、SKIPIF1<0、SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為SKIPIF1<0.題型一：零點(diǎn)存在定理法判斷函數(shù)零點(diǎn)所在區(qū)間一、單選題1．（2022·河南河南·三模（理））若實(shí)數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·黑龍江·雙鴨山一中高三期末（理））函數(shù)SKIPIF1<0的零點(diǎn)所在的區(qū)間為（

）SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·北京密云·高三期末）心理學(xué)家有時使用函數(shù)SKIPIF1<0來測定在時間SKIPIF1<0內(nèi)能夠記憶的量SKIPIF1<0，其中A表示需要記憶的量，SKIPIF1<0表示記憶率．假設(shè)一個學(xué)生有200個單詞要記憶，心理學(xué)家測定在5min內(nèi)該學(xué)生記憶20個單詞．則記憶率SKIPIF1<0所在區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·河南焦作·一模（理））設(shè)函數(shù)SKIPIF1<0的零點(diǎn)為SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2021·江蘇·泰州中學(xué)高三階段練習(xí)）已知SKIPIF1<0，函數(shù)SKIPIF1<0的零點(diǎn)為SKIPIF1<0，SKIPIF1<0的極小值點(diǎn)為SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·安徽·安慶一中高三期末（理））函數(shù)SKIPIF1<0的零點(diǎn)所在的區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題7．（2022·湖北·荊州中學(xué)高三開學(xué)考試）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0的最小值為SKIPIF1<0，且在區(qū)間SKIPIF1<0唯一的極大值點(diǎn)SKIPIF1<0．則下列說法正確的有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2022·全國·高三專題練習(xí)）設(shè)函數(shù)SKIPIF1<0的定義域為R，如果存在常數(shù)SKIPIF1<0，對于任意SKIPIF1<0，都有SKIPIF1<0，則稱函數(shù)SKIPIF1<0是“類周期函數(shù)”，T為函數(shù)SKIPIF1<0的“類周期”．現(xiàn)有下面四個命題，正確的是（

）A．函數(shù)SKIPIF1<0是“類周期函數(shù)”B．函數(shù)SKIPIF1<0是“類周期函數(shù)”C．如果函數(shù)SKIPIF1<0是“類周期函數(shù)”，那么“SKIPIF1<0，SKIPIF1<0”D．如果“類周期函數(shù)”SKIPIF1<0的“類周期”為SKIPIF1<0，那么它是周期為2的周期函數(shù)9．（2021·江西·模擬預(yù)測）已知實(shí)數(shù)SKIPIF1<0，設(shè)方程SKIPIF1<0的兩個實(shí)數(shù)根分別為SKIPIF1<0，則下列結(jié)論正確的是（

）A．不等式SKIPIF1<0的解集為SKIPIF1<0B．不等式SKIPIF1<0的解集可能為空集C．SKIPIF1<0D．SKIPIF1<0三、填空題10．（2022·全國·高三專題練習(xí)）下列命題中，正確的是___________．(寫出所有正確命題的編號)①在SKIPIF1<0中，SKIPIF1<0是SKIPIF1<0的充要條件；②函數(shù)SKIPIF1<0的最大值是SKIPIF1<0；③若命題“SKIPIF1<0，使得SKIPIF1<0”是假命題，則SKIPIF1<0；④若函數(shù)SKIPIF1<0，SKIPIF1<0，則函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)必有零點(diǎn)．11．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)，下列命題：①存在實(shí)數(shù)SKIPIF1<0，使得導(dǎo)函數(shù)SKIPIF1<0為增函數(shù)；②當(dāng)SKIPIF1<0時，函數(shù)SKIPIF1<0不單調(diào)；③當(dāng)SKIPIF1<0時，函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減；④當(dāng)SKIPIF1<0時，函數(shù)SKIPIF1<0有極值．在以上命題中，正確的命題序號是______．12．（2021·福建·三明一中高三學(xué)業(yè)考試）已知函數(shù)SKIPIF1<0的零點(diǎn)SKIPIF1<0，則SKIPIF1<0__________．13．（2022·全國·高三專題練習(xí)）已知SKIPIF1<0，SKIPIF1<0均為正實(shí)數(shù)，且滿足SKIPIF1<0，SKIPIF1<0，則下面四個判斷：①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0；④SKIPIF1<0.其中一定成立的有__（填序號即可）.14．（2020·湖南邵陽·三模（理））在數(shù)學(xué)中，布勞威爾不動點(diǎn)定理是拓樸學(xué)里一個非常重要的不動點(diǎn)定理，它可應(yīng)用到有限維空間并構(gòu)成了一般不動點(diǎn)定理的基石，簡單來講就是對于滿足一定條件的連續(xù)函數(shù)SKIPIF1<0，存在一個點(diǎn)SKIPIF1<0，使SKIPIF1<0，那么我們稱該函數(shù)SKIPIF1<0為“不動點(diǎn)”函數(shù)，給出下列函數(shù)：①SKIPIF1<0；②SKIPIF1<0③SKIPIF1<0；④SKIPIF1<0（SKIPIF1<0）；⑤SKIPIF1<0；其中為“不動點(diǎn)”函數(shù)的是_________.（寫出所有滿足條件的函數(shù)的序號）15．（2020·全國·高三專題練習(xí)（理））函數(shù)f(x)＝1＋x－SKIPIF1<0＋SKIPIF1<0，g(x)＝1－x＋SKIPIF1<0－SKIPIF1<0，若函數(shù)F(x)＝f(x＋3)g(x－4)，且函數(shù)F(x)的零點(diǎn)均在[a，b](a<b，a，b∈Z)內(nèi)，則b－a的最小值為________.四、解答題16．（2022·陜西西安·高三階段練習(xí)（文））已知函數(shù)SKIPIF1<0（e為自然對數(shù)的底數(shù)，SKIPIF1<0）.(1)若SKIPIF1<0，求證：SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)有唯一零點(diǎn)；(2)若SKIPIF1<0在其定義域上單調(diào)遞減，求a的取值范圍.17．（2022·貴州遵義·高三開學(xué)考試（理））已知函數(shù)SKIPIF1<0.(1)討論SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0零點(diǎn)的個數(shù)；(2)若SKIPIF1<0的最小值為e，求a的取值范圍.題型二：方程法判斷零點(diǎn)個數(shù)一、單選題1．（2022·福建福州·三模）已知函數(shù)SKIPIF1<0，以下結(jié)論中錯誤的是（

）A．SKIPIF1<0是偶函數(shù) B．SKIPIF1<0有無數(shù)個零點(diǎn)C．SKIPIF1<0的最小值為SKIPIF1<0 D．SKIPIF1<0的最大值為SKIPIF1<02．（2022·北京·模擬預(yù)測）已知函數(shù)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的零點(diǎn)個數(shù)為（

）A．SKIPIF1<0個 B．SKIPIF1<0個 C．SKIPIF1<0個 D．SKIPIF1<0個3．（2022·安徽·蕪湖一中一模（理））聲音是由物體振動產(chǎn)生的聲波，我們聽到的聲音中包含著正弦函數(shù)．若某聲音對應(yīng)的函數(shù)可近似為SKIPIF1<0，則下列敘述正確的是（

）A．SKIPIF1<0為SKIPIF1<0的對稱軸 B．SKIPIF1<0為SKIPIF1<0的對稱中心C．SKIPIF1<0在區(qū)間SKIPIF1<0上有3個零點(diǎn) D．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增4．（2022·全國·高三專題練習(xí)）已知函數(shù)f(x)=x+2,x<1,x+2x,x≥1.，則函數(shù)A．0 B．1 C．2 D．3二、多選題5．（2022·海南?？凇つM預(yù)測）已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0的定義域為R B．SKIPIF1<0是奇函數(shù)C．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減 D．SKIPIF1<0有兩個零點(diǎn)6．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，下列說法正確的是（

）.A．SKIPIF1<0是周期函數(shù)B．若SKIPIF1<0，則SKIPIF1<0（SKIPIF1<0）C．SKIPIF1<0在區(qū)間SKIPIF1<0上是增函數(shù)D．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有且僅有一個零點(diǎn)7．（2022·全國·高三專題練習(xí)）若SKIPIF1<0和SKIPIF1<0都是定義在SKIPIF1<0上的函數(shù)，且方程SKIPIF1<0有實(shí)數(shù)解，則下列式子中可以為SKIPIF1<0的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2022·全國·高三專題練習(xí)（理））關(guān)于函數(shù)SKIPIF1<0有下述四個結(jié)論，則（

）A．SKIPIF1<0是偶函數(shù) B．SKIPIF1<0的最小值為SKIPIF1<0C．SKIPIF1<0在SKIPIF1<0上有4個零點(diǎn) D．SKIPIF1<0在區(qū)間SKIPIF1<0單調(diào)遞增三、填空題9．（2022·福建·模擬預(yù)測）已知函數(shù)SKIPIF1<0，其中SKIPIF1<0，若SKIPIF1<0在區(qū)間(SKIPIF1<0，SKIPIF1<0)上恰有2個零點(diǎn)，則SKIPIF1<0的取值范圍是____________.10．（2022·河南·襄城縣教育體育局教學(xué)研究室二模（文））已知函數(shù)SKIPIF1<0有3個零點(diǎn)，則實(shí)數(shù)m的取值范圍為______．四、解答題11．（2022·全國·模擬預(yù)測（文））已知函數(shù)SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性；(2)當(dāng)SKIPIF1<0時，證明SKIPIF1<0在SKIPIF1<0上有且僅有兩個零點(diǎn).12．（2022·四川省高縣中學(xué)校模擬預(yù)測（文））已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時，判定SKIPIF1<0的零點(diǎn)的個數(shù)；(2)是否存在實(shí)數(shù)SKIPIF1<0，使得當(dāng)SKIPIF1<0時，SKIPIF1<0恒成立？若存在，求出SKIPIF1<0的取值范圍；若不存在，請說明理由.題型三：數(shù)形結(jié)合法判段函數(shù)零點(diǎn)個數(shù)一、單選題1．（2022·安徽淮南·二模（文））已知函數(shù)，則下列關(guān)于函數(shù)的描述中，其中正確的是（

）．①當(dāng)時，函數(shù)沒有零點(diǎn)；②當(dāng)時，函數(shù)有兩不同零點(diǎn)，它們互為倒數(shù)；③當(dāng)時，函數(shù)有兩個不同零點(diǎn)；④當(dāng)時，函數(shù)有四個不同零點(diǎn)，且這四個零點(diǎn)之積為1．A．①② B．②③ C．②④ D．③④2．（2022·河南安陽·模擬預(yù)測（文））已知函數(shù)，則關(guān)于的方程有個不同實(shí)數(shù)解，則實(shí)數(shù)滿足（

）A．且 B．且C．且 D．且3．（2022·安徽·模擬預(yù)測（文））已知函數(shù)，若有4個零點(diǎn)，則實(shí)數(shù)a的取值范圍是（

）A． B． C． D．4．（2022·河南河南·三模（理））函數(shù)的所有零點(diǎn)之和為（

）A．0 B．2 C．4 D．6二、多選題5．（2022·廣東·普寧市華僑中學(xué)二模）對于函數(shù)，下列結(jié)論中正確的是（

）A．任取，都有B．，其中；C．對一切恒成立；D．函數(shù)有個零點(diǎn)；6．（2022·江蘇·南京市寧海中學(xué)模擬預(yù)測）已知是定義在R上的偶函數(shù)，且對任意，有，當(dāng)時，，則（

）A．是以2為周期的周期函數(shù)B．點(diǎn)是函數(shù)的一個對稱中心C．D．函數(shù)有3個零點(diǎn)三、填空題7．（2022·四川·成都七中三模（文））已知函數(shù)，則函數(shù)的零點(diǎn)個數(shù)是______個．8．（2022·內(nèi)蒙古呼和浩特·一模（理））下面四個命題：①已知函數(shù)的定義域為，若為偶函數(shù)，為奇函數(shù)，則；②存在負(fù)數(shù)，使得恰有3個零點(diǎn)；③已知多項式，則；④設(shè)一組樣本數(shù)據(jù)的方差為，則數(shù)據(jù)的方差為其中真命題的序號為___________.9．（2022·四川成都·二模（文））定義在R上的奇函數(shù)f（x）滿足，且當(dāng)時，．則函數(shù)的所有零點(diǎn)之和為______．10．（2022·全國·高三專題練習(xí)）已知，給出下列四個結(jié)論：（1）若，則有兩個零點(diǎn)；（2），使得有一個零點(diǎn)；（3），使得有三個零點(diǎn)；（4），使得有三個零點(diǎn)．以上正確結(jié)論的序號是__．四、解答題11．（2022·北京·高三學(xué)業(yè)考試）給定集合，為定義在D上的函數(shù)，當(dāng)時，，且對任意，都有___________．從條件①、條件②、條件③這三個條件中選擇一個作為已知，補(bǔ)充在橫線處，使存在且唯一確定．條件①：；條件②：；條件③：．解答下列問題：（1）寫出和的值；（2）寫出在上的單調(diào)區(qū)間；（3）設(shè)，寫出的零點(diǎn)個數(shù)．12．（2021·河北·高三階段練習(xí)）已知函數(shù)的最小正周期為.（1）求函數(shù)的單調(diào)遞增區(qū)間；（2）若先將函數(shù)圖像上所有點(diǎn)的橫坐標(biāo)伸長為原來的2倍（縱坐標(biāo)不變），再將其圖像向左平移個單位長度，得到函數(shù)的圖像，求方程在上根的個數(shù).13．（2021·遼寧·高三階段練習(xí)）已知函數(shù)的最小正周期為．（I）求函數(shù)的解析式；（II）若先將函數(shù)的圖象向左平移個單位長度，再將其圖象上所有點(diǎn)的橫坐標(biāo)伸長為原來的倍（縱坐標(biāo)不變），得到函數(shù)的圖象，求在上的零點(diǎn)個數(shù)．題型四：轉(zhuǎn)化法判斷函數(shù)零點(diǎn)個數(shù)一、單選題1．（2022·安徽·巢湖市第一中學(xué)高三期中（文））已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為（

）A．3 B．4 C．5 D．62．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為（

）A．3 B．4 C．2 D．13．（2021·天津市實(shí)驗中學(xué)濱海學(xué)校高三期中）已知函數(shù)SKIPIF1<0則函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)不可能是（

）A．1 B．2 C．3 D．44．（2021·遼寧沈陽·高三階段練習(xí)）對于任意正實(shí)數(shù)SKIPIF1<0，關(guān)于SKIPIF1<0的方程SKIPIF1<0的解集不可能是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題5．（2022·江蘇無錫·高三期末）高斯被人認(rèn)為是歷史上最重要的數(shù)學(xué)家之一，并享有“數(shù)學(xué)王子”之稱.有這樣一個函數(shù)就是以他名字命名的：設(shè)SKIPIF1<0，用SKIPIF1<0表示不超過SKIPIF1<0的最大整數(shù)，則SKIPIF1<0稱為高斯函數(shù)，又稱為取整函數(shù).如：SKIPIF1<0，SKIPIF1<0.則下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0是SKIPIF1<0上的單調(diào)遞增函數(shù)B．函數(shù)SKIPIF1<0有SKIPIF1<0個零點(diǎn)C．SKIPIF1<0是SKIPIF1<0上的奇函數(shù)D．對于任意實(shí)數(shù)SKIPIF1<0，都有SKIPIF1<06．（2022·全國·高三專題練習(xí)）定義域和值域均為SKIPIF1<0（常數(shù)SKIPIF1<0）的函數(shù)SKIPIF1<0和SKIPIF1<0圖象如圖所示，給出下列四個命題，那么，其中正確命題是（

）A．方程SKIPIF1<0有且僅有三個解B．方程SKIPIF1<0有且僅有三個解C．方程SKIPIF1<0有且僅有九個解D．方程SKIPIF1<0有且僅有一個解三、填空題7．（2022·全國·高三專題練習(xí)）已知SKIPIF1<0是定義在R上的奇函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0=SKIPIF1<0，則方程SKIPIF1<0解的個數(shù)為___________.8．（2021·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0若直線SKIPIF1<0與函數(shù)SKIPIF1<0的圖象交于A，B兩點(diǎn)，且滿足SKIPIF1<0，其中O為坐標(biāo)原點(diǎn)，則k值的個數(shù)為___________.四、解答題9．（2021·全國·高三專題練習(xí)）證明：函數(shù)SKIPIF1<0的圖象與SKIPIF1<0的圖象有且僅有一個公共點(diǎn)．10．（2020·安徽·淮南市第五中學(xué)高三階段練習(xí)（理））已知SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0（1）求SKIPIF1<0，SKIPIF1<0的值；（2）求SKIPIF1<0的解析式并畫出函數(shù)的簡圖；（3）討論方程SKIPIF1<0的根的情況.題型五：零點(diǎn)存在定理與函數(shù)性質(zhì)結(jié)合判斷零點(diǎn)個數(shù)一、單選題1．（2022·廣東韶關(guān)·二模）已知直線SKIPIF1<0既是函數(shù)SKIPIF1<0的圖象的切線，同時也是函數(shù)SKIPIF1<0的圖象的切線，則函數(shù)SKIPIF1<0零點(diǎn)個數(shù)為（

）A．0 B．1 C．0或1 D．1或22．（2022·天津·高三專題練習(xí)）設(shè)函數(shù)SKIPIF1<0有5個不同的零點(diǎn)，則正實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·高三專題練習(xí)（理））已知函數(shù)SKIPIF1<0有兩個零點(diǎn)，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題4．（2021·江蘇·泰州中學(xué)高三階段練習(xí)）已知函數(shù)f(x)＝sin(|cosx|)＋cos(|sinx|)，則以下結(jié)論正確的是（

）A．f(x)的圖象關(guān)于直線SKIPIF1<0對稱 B．f(x)是最小正周期為2π的偶函數(shù)C．f(x)在區(qū)間SKIPIF1<0上單調(diào)遞減 D．方程SKIPIF1<0恰有三個不相等的實(shí)數(shù)根5．（2021·湖北恩施·高三開學(xué)考試）已知函數(shù)SKIPIF1<0，則以下說法正確的是（

）A．SKIPIF1<0是偶函數(shù)B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增C．當(dāng)SKIPIF1<0時，SKIPIF1<0D．方程SKIPIF1<0有且只有兩個實(shí)根6．（2022·全國·高三專題練習(xí)）函數(shù)SKIPIF1<0，則下列說法正確的有（

）A．函數(shù)SKIPIF1<0是SKIPIF1<0上的單調(diào)遞增函數(shù)B．對于任意實(shí)數(shù)SKIPIF1<0，不等式SKIPIF1<0恒成立C．若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0D．方程SKIPIF1<0有3個不相等實(shí)數(shù)解三、解答題7．（2022·江西南昌·二模（文））已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)若SKIPIF1<0，證明：方程SKIPIF1<0有且僅有一個正根.8．（2022·河北·模擬預(yù)測）已知函數(shù)SKIPIF1<0.(1)請研究函數(shù)SKIPIF1<0在SKIPIF1<0上的零點(diǎn)個數(shù)并證明；(2)當(dāng)SKIPIF1<0時，證明：SKIPIF1<0.9．（2022·全國·高三專題練習(xí)）設(shè)SKIPIF1<0為實(shí)數(shù)，函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，求SKIPIF1<0的取值范圍；(2)討論SKIPIF1<0的單調(diào)性；(3)當(dāng)SKIPIF1<0時，討論SKIPIF1<0在SKIPIF1<0上的零點(diǎn)個數(shù).10．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，求函數(shù)SKIPIF1<0在SKIPIF1<0上的零點(diǎn)個數(shù)；(2)當(dāng)SKIPIF1<0時都有SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍.題型六：利用函數(shù)零點(diǎn)（方程有根）求參數(shù)值或參數(shù)范圍一、單選題1．（2022·四川成都·三模（理））若函數(shù)SKIPIF1<0的零點(diǎn)為SKIPIF1<0，則SKIPIF1<0（

）．A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．22．（2022·湖南岳陽·三模）已知函數(shù)SKIPIF1<0，若不等式SKIPIF1<0有且僅有2個整數(shù)解，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·山西·模擬預(yù)測（文））已知函數(shù)SKIPIF1<0若函數(shù)SKIPIF1<0有三個零點(diǎn)，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題4．（2021·遼寧·東北育才學(xué)校二模）一般地，若函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，值域為SKIPIF1<0，則稱為的“SKIPIF1<0倍跟隨區(qū)間”；若函數(shù)的定義域為SKIPIF1<0，值域也為SKIPIF1<0，則稱SKIPIF1<0為SKIPIF1<0的“跟隨區(qū)間”.下列結(jié)論正確的是（

）A．若SKIPIF1<0為SKIPIF1<0的跟隨區(qū)間，則SKIPIF1<0B．函數(shù)SKIPIF1<0存在跟隨區(qū)間C．若函數(shù)SKIPIF1<0存在跟隨區(qū)間，則SKIPIF1<0D．二次函數(shù)SKIPIF1<0存在“3倍跟隨區(qū)間”三、填空題5．（2022·福建南平·三模）已知函數(shù)SKIPIF1<0有零點(diǎn)，則實(shí)數(shù)SKIPIF1<0___________.6．（2022·四川·石室中學(xué)三模（文））若函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，且直線SKIPIF1<0與函數(shù)SKIPIF1<0的圖象有三個不同的公共點(diǎn)，則實(shí)數(shù)k的值為______．四、解答題7．（2021·遼寧·東北育才學(xué)校二模）已知二次函數(shù)SKIPIF1<0滿足以下條件：①經(jīng)過原點(diǎn)SKIPIF1<0;②SKIPIF1<0，SKIPIF1<0;③函數(shù)SKIPIF1<0只有一個零點(diǎn)(1)求二次函數(shù)SKIPIF1<0的解析式；(2)若函數(shù)SKIPIF1<0與SKIPIF1<0的圖象有兩個公共點(diǎn)，求實(shí)數(shù)SKIPIF1<0的取值范圍.題型七：利用函數(shù)的交點(diǎn)（交點(diǎn)個數(shù)）求參數(shù)一、單選題1．（2022·河南安陽·模擬預(yù)測（理））已知函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0），若函數(shù)SKIPIF1<0的零點(diǎn)有5個，則實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022·山東濟(jì)寧·二模）已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0有5個零點(diǎn)，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·模擬預(yù)測（理））已知函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，對SKIPIF1<0，都有SKIPIF1<0恒成立，當(dāng)SKIPIF1<0時，SKIPIF1<0，當(dāng)SKIPIF1<0時，若函數(shù)SKIPIF1<