新高考數(shù)學(xué)一輪復(fù)習(xí)精講精練8.10 零點(diǎn)定理（基礎(chǔ)版）（原卷版）

8.10零點(diǎn)定理（精講）（基礎(chǔ)版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一零點(diǎn)的求解【例1】（2022·廣東）函數(shù)SKIPIF1<0的零點(diǎn)為（

）A．10 B．9 C．（10，0） D．（9，0）【一隅三反】1．（2022·廣西）若SKIPIF1<0是函數(shù)SKIPIF1<0的一個零點(diǎn)，則SKIPIF1<0的另一個零點(diǎn)為（

）A．1 B．2 C．（1，0） D．（2，0）2．（2023·全國·高三專題練習(xí)）已知數(shù)列SKIPIF1<0為等比數(shù)列，若SKIPIF1<0，SKIPIF1<0為函數(shù)SKIPIF1<0的兩個零點(diǎn)，則SKIPIF1<0（

）A．10 B．12 C．32 D．333．（2022·貴州）函數(shù)SKIPIF1<0的零點(diǎn)為（

）A．2 B．1 C．0 D．SKIPIF1<04．（2022·云南）函數(shù)f（x）＝x2﹣4x+4的零點(diǎn)是（）A．（0，2） B．（2，0） C．2 D．4考點(diǎn)二零點(diǎn)區(qū)間【例2】（2022高三上·安徽期末）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【一隅三反】1．（2022高三上·青島期中）方程SKIPIF1<0的實(shí)數(shù)根所在的區(qū)間為()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·大連模擬）函數(shù)SKIPIF1<0，在下列區(qū)間中，包含函數(shù)SKIPIF1<0零點(diǎn)的區(qū)間為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2021高三上·河南期中）下列區(qū)間一定包含函數(shù)SKIPIF1<0的零點(diǎn)的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)三零點(diǎn)的個數(shù)【例3-1】（2022·呂梁模擬）函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為（）A．1 B．2 C．3 D．4【例3-2】（2022·延慶模擬）已知函數(shù)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的零點(diǎn)個數(shù)為（）A．1個 B．2個 C．3個 D．4個【例3-3】（2021·西安模擬）函數(shù)SKIPIF1<0在區(qū)間（0，1）內(nèi)的零點(diǎn)個數(shù)是（）A．0 B．1 C．2 D．3【一隅三反】1．（2021·云南模擬）函數(shù)SKIPIF1<0在SKIPIF1<0上的零點(diǎn)個數(shù)為（）A．2 B．3 C．4 D．52．（2022·安徽宣城）函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為（

）A．1 B．2 C．3 D．43（2022·重慶·三模）已知函數(shù)SKIPIF1<0，則函數(shù)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4．（2022·全國·課時練習(xí)）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的零點(diǎn)個數(shù)為（

）A．6 B．5 C．4 D．3考點(diǎn)四求參數(shù)【例4-1】（2022·昌平模擬）若函數(shù)SKIPIF1<0有且僅有兩個零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的一個取值為.【例4-2】（2022高三上·西寧期末）已知函數(shù)f(x)=lnx，x>0，?xA．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2021·江蘇）若方程SKIPIF1<0，且SKIPIF1<0有兩個不同實(shí)數(shù)根，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高三專題練習(xí)）已知SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0在區(qū)間SKIPIF1<0上恰有4個零點(diǎn)，則實(shí)數(shù)a的取值范圍是（

）A．（1，3） B．（2，4） C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·課時練習(xí)）已知函數(shù)SKIPIF1<0有零點(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<04．（2022·北京大興）若函數(shù)SKIPIF1<0恰有SKIPIF1<0個零點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08.10零點(diǎn)定理（精練）（基礎(chǔ)版）題組一題組一零點(diǎn)的求解1．（2022·上海）若函數(shù)SKIPIF1<0的零點(diǎn)為2，則函數(shù)SKIPIF1<0的零點(diǎn)是（

）A．0，SKIPIF1<0 B．0，SKIPIF1<0 C．0，2 D．2，SKIPIF1<02．（2022·北京）已知SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0的零點(diǎn)個數(shù)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．不能確定3．（2022·福建福州）（多選）已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)是（

）A．-1 B．0 C．1 D．24．（2021高三上·吉林月考）（多選）等比數(shù)列SKIPIF1<0中，SKIPIF1<0與SKIPIF1<0是函數(shù)SKIPIF1<0的兩個零點(diǎn)，則SKIPIF1<0的值為（）A．-2 B．2 C．-5 D．55．（2022·全國·專題練習(xí)）函數(shù)SKIPIF1<0的零點(diǎn)是___．6．（2022·福建·廈門外國語學(xué)校）已知函數(shù)SKIPIF1<0則方程SKIPIF1<0的根___________.7．（2022·廣東·佛山市南海區(qū)桂城中學(xué)）函數(shù)SKIPIF1<0的導(dǎo)數(shù)的零點(diǎn)組成的集合為___________.題組二題組二零點(diǎn)區(qū)間1．（2021高三上·陜西月考）函數(shù)SKIPIF1<0的零點(diǎn)所在的一個區(qū)間是（）A．(1，2) B．(2，3) C．(3，4) D．(4，5)2．（2021高三上·月考）下列區(qū)間中，包含函數(shù)SKIPIF1<0的零點(diǎn)的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022高三上·興寧期末）若SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022高三上·遼寧期中）已知函數(shù)SKIPIF1<0，那么在下列區(qū)間中含有函數(shù)SKIPIF1<0零點(diǎn)的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022高三上·海安月考）函數(shù)SKIPIF1<0的零點(diǎn)所在的大致區(qū)間是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題組三題組三零點(diǎn)的個數(shù)1．（2022高三上·河南期中）已知函數(shù)f(x)=x2?2x，x≥0x?4x，x<0A．1 B．2 C．3 D．42．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0，SKIPIF1<0的零點(diǎn)個數(shù)（）A．5或6個 B．3或9個 C．9或10個 D．5或9個3．（2022·黑龍江）已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)是（

）A．4 B．5 C．6 D．74．（2023·全國·高三專題練習(xí)）若定義在R上的偶函數(shù)f(x)滿足f(x＋2)＝f(x)，且當(dāng)x∈[0,1]時，f(x)＝x，則函數(shù)y＝f(x)－log3|x|的零點(diǎn)個數(shù)是（

）A．1 B．2 C．3 D．45．（2022·西安模擬）已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)至少為（）A．3 B．4 C．5 D．66．（2022·新疆三模）函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為.7．（2022·全國·課時練習(xí)）函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為________．8．（2022·全國·課時練習(xí)）函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)為________．9．（2022·河南·鄭州十九中高三階段練習(xí)（文））已知函數(shù)SKIPIF1<0則函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)是___________.10．（2023·全國·高三專題練習(xí)）若偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，在SKIPIF1<0時，SKIPIF1<0，則關(guān)于x的方程SKIPIF1<0在SKIPIF1<0上根的個數(shù)是___．11．（2022·全國·專題練習(xí)）奇函數(shù)SKIPIF1<0定義在SKIPIF1<0上，且對常數(shù)SKIPIF1<0，恒有SKIPIF1<0，則在區(qū)間SKIPIF1<0上，方程SKIPIF1<0根的個數(shù)最小值為_______.12．（2022·全國·專題練習(xí)）已知函數(shù)SKIPIF1<0圖象關(guān)于直線SKIPIF1<0對稱，則函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上零點(diǎn)的個數(shù)為____