新高考數(shù)學(xué)一輪復(fù)習(xí) 函數(shù)專項(xiàng)重難點(diǎn)突破專題15 函數(shù)零點(diǎn)問題(原卷版)

專題15函數(shù)零點(diǎn)問題真題呈現(xiàn)1．（2021·天津·統(tǒng)考高考真題）設(shè)SKIPIF1<0，函數(shù)SKIPIF1<0，若SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)恰有6個零點(diǎn)，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023·全國·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0有且僅有3個零點(diǎn)，則SKIPIF1<0的取值范圍是________．3．（2023·天津·統(tǒng)考高考真題）若函數(shù)SKIPIF1<0有且僅有兩個零點(diǎn)，則SKIPIF1<0的取值范圍為___．4．（2022·天津·統(tǒng)考高考真題）設(shè)SKIPIF1<0，對任意實(shí)數(shù)x，記SKIPIF1<0．若SKIPIF1<0至少有3個零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍為______.5．（2021·北京·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0，給出下列四個結(jié)論：①若SKIPIF1<0，SKIPIF1<0恰有2個零點(diǎn)；②存在負(fù)數(shù)SKIPIF1<0，使得SKIPIF1<0恰有1個零點(diǎn)；③存在負(fù)數(shù)SKIPIF1<0，使得SKIPIF1<0恰有3個零點(diǎn)；④存在正數(shù)SKIPIF1<0，使得SKIPIF1<0恰有3個零點(diǎn)．其中所有正確結(jié)論的序號是_______．6．（2022·北京·統(tǒng)考高考真題）若函數(shù)SKIPIF1<0的一個零點(diǎn)為SKIPIF1<0，則SKIPIF1<0_____；SKIPIF1<0__．考點(diǎn)一函數(shù)零點(diǎn)的定義一、單選題1．函數(shù)SKIPIF1<0的零點(diǎn)為（

）A．2，3 B．2 C．SKIPIF1<0 D．SKIPIF1<02．若SKIPIF1<0是二次函數(shù)SKIPIF1<0的兩個零點(diǎn)，則SKIPIF1<0的值是（）A．3 B．15 C．SKIPIF1<0 D．SKIPIF1<03．關(guān)于SKIPIF1<0的函數(shù)SKIPIF1<0的兩個零點(diǎn)為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0＝（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．若向量SKIPIF1<0，SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<05．函數(shù)SKIPIF1<0有且只有一個零點(diǎn)，則實(shí)數(shù)m的值為（

）A．9 B．12 C．0或9 D．0或12二、填空題6．函數(shù)SKIPIF1<0的零點(diǎn)為________．7．若函數(shù)SKIPIF1<0有且僅有兩個零點(diǎn)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0_______.三、解答題8．求下列函數(shù)的零點(diǎn)．(1)SKIPIF1<0；(2)SKIPIF1<0.考點(diǎn)二零點(diǎn)存在定理判斷零點(diǎn)所在區(qū)間一、單選題1．函數(shù)SKIPIF1<0的零點(diǎn)所在區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知方程SKIPIF1<0的解在SKIPIF1<0內(nèi)，則SKIPIF1<0（

）A．3 B．2 C．1 D．03．已知函數(shù)SKIPIF1<0，則SKIPIF1<0的零點(diǎn)所在的區(qū)間為（

）.A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的零點(diǎn)必屬于區(qū)間（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知SKIPIF1<0唯一的零點(diǎn)同時在區(qū)間SKIPIF1<0和SKIPIF1<0內(nèi)，下列說法錯誤的是（

）A．函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)有零點(diǎn) B．函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)無零點(diǎn)C．函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)有零點(diǎn) D．函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)無零點(diǎn)6．已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0的實(shí)根在區(qū)間SKIPIF1<0上，則k的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的圖象過定點(diǎn)SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)所在區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題8．函數(shù)SKIPIF1<0的零點(diǎn)所在區(qū)間（取整數(shù)）是_________．考點(diǎn)三求函數(shù)零點(diǎn)個數(shù)一、單選題1．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的零點(diǎn)個數(shù)是（

）A．3 B．4 C．5 D．62．函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為（

）A．1 B．3 C．5 D．73．函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為（

）A．0個 B．1個 C．2個 D．3個4．函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為（

）A．2 B．3 C．4 D．55．已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0零點(diǎn)個數(shù)為（

）A．0 B．1 C．2 D．36．設(shè)函數(shù)SKIPIF1<0若SKIPIF1<0,SKIPIF1<0,則關(guān)于SKIPIF1<0的方程SKIPIF1<0的解的個數(shù)為（

）A．1 B．2 C．3 D．47．方程SKIPIF1<0，SKIPIF1<0實(shí)根的個數(shù)為（

）A．6 B．5 C．4 D．38．已知函數(shù)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0在區(qū)間SKIPIF1<0上的零點(diǎn)個數(shù)為（

）A．1 B．2 C．3 D．49．已知定義域?yàn)镾KIPIF1<0的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，若將方程SKIPIF1<0實(shí)數(shù)解的個數(shù)記為SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、填空題10．函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)是__________．11．已知SKIPIF1<0，方程SKIPIF1<0的實(shí)根個數(shù)為__________．12．定義在R上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則函數(shù)SKIPIF1<0有__________個零點(diǎn)．考點(diǎn)四根據(jù)函數(shù)零點(diǎn)求參一、單選題1．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．已知函數(shù)SKIPIF1<0，若SKIPIF1<0恰有兩個零點(diǎn)，則正數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知函數(shù)SKIPIF1<0（e為自然對數(shù)的底數(shù)，a∈R）有3個不同的零點(diǎn)，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．已知函數(shù)SKIPIF1<0，若SKIPIF1<0有3個不同的解，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．已知函數(shù)SKIPIF1<0若函數(shù)SKIPIF1<0有五個零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0有四個不同的實(shí)數(shù)根，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．若函數(shù)SKIPIF1<0SKIPIF1<0恰有2個零點(diǎn)，則實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題8．已知函數(shù)SKIPIF1<0，實(shí)數(shù)SKIPIF1<0、SKIPIF1<0是函數(shù)SKIPIF1<0的兩個零點(diǎn)，則下列結(jié)論正確的有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0且方程SKIPIF1<0的6個解分別為SKIPIF1<0SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空題10．設(shè)函數(shù)SKIPIF1<0在區(qū)間[SKIPIF1<0上有零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是___________.11．函數(shù)SKIPIF1<0在SKIPIF1<0上存在零點(diǎn)，則整數(shù)t的值為______．12．若函數(shù)SKIPIF1<0