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3.6零點(diǎn)定理（精講）（提升版）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)的區(qū)間【例1】（2022·河南開(kāi)封·）函數(shù)SKIPIF1<0的一個(gè)零點(diǎn)所在的區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·湖南）函數(shù)SKIPIF1<0的零點(diǎn)所在區(qū)間是（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<02．（2022·四川攀枝花）已知函數(shù)SKIPIF1<0的零點(diǎn)在區(qū)間SKIPIF1<0上，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·云南德宏）方程SKIPIF1<0的解所在的區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)二零點(diǎn)的個(gè)數(shù)【例2-1】（2022·陜西）函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)為（

）A．0 B．1 C．2 D．3【例2-2】（2022·山西）已知SKIPIF1<0若SKIPIF1<0，則SKIPIF1<0在SKIPIF1<0內(nèi)的零點(diǎn)個(gè)數(shù)為（

）A．8 B．9 C．10 D．11【一隅三反】1．（2022·安徽）已知函數(shù)SKIPIF1<0則方程SKIPIF1<0的解的個(gè)數(shù)是（

）A．0 B．1 C．2 D．32．（2022·全國(guó)·高三專(zhuān)題練習(xí)）函數(shù)SKIPIF1<0的圖像與函數(shù)SKIPIF1<0的圖像的交點(diǎn)個(gè)數(shù)為（

）A．2 B．3 C．4 D．03．（2022·海南?。┰O(shè)函數(shù)SKIPIF1<0定義域?yàn)镽，SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則函數(shù)SKIPIF1<0有（

）個(gè)零點(diǎn)A．4 B．5 C．6 D．7考點(diǎn)三比較零點(diǎn)的大小【例3】（2022·安徽）已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的零點(diǎn)分別為a，b，c則a，b，c的大小順序?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·河南）若實(shí)數(shù)SKIPIF1<0滿足SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·安徽）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·山西）正實(shí)數(shù)SKIPIF1<0滿足SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0之間的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)四已知零點(diǎn)求參數(shù)【例4-1】（2022·山東濰坊）已知函數(shù)SKIPIF1<0的圖像與直線SKIPIF1<0有3個(gè)不同的交點(diǎn)，則實(shí)數(shù)m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例4-2】（2022·吉林）已知SKIPIF1<0若關(guān)于x的方程SKIPIF1<0有3個(gè)不同實(shí)根，則實(shí)數(shù)SKIPIF1<0取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例4-3】（2022·安徽·合肥市）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有且僅有4個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知函數(shù)SKIPIF1<0若關(guān)于x的方程SKIPIF1<0恰有三個(gè)不相等的實(shí)數(shù)解，則m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南·模擬預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0為定義在SKIPIF1<0上的單調(diào)函數(shù)，且SKIPIF1<0．若函數(shù)SKIPIF1<0有3個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·廣西·貴港市高級(jí)中學(xué)三模）已知SKIPIF1<0在SKIPIF1<0有且僅有6個(gè)實(shí)數(shù)根，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·山西）已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0恰好有兩個(gè)零點(diǎn)，則實(shí)數(shù)k的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)五零點(diǎn)的綜合運(yùn)用【例5-1】（2022·新疆克拉瑪依）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的所有零點(diǎn)之和為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例5-2】（2022·甘肅）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有2個(gè)零點(diǎn)SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例5-3】（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知函數(shù)SKIPIF1<0的零點(diǎn)為SKIPIF1<0，函數(shù)SKIPIF1<0的零點(diǎn)為SKIPIF1<0，則下列不等式中成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·安徽·合肥一六八中學(xué)）若SKIPIF1<0為奇函數(shù)，且SKIPIF1<0是SKIPIF1<0的一個(gè)零點(diǎn)，則SKIPIF1<0一定是下列哪個(gè)函數(shù)的零點(diǎn)（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·陜西·模擬預(yù)測(cè)（理））已知SKIPIF1<0是方程SKIPIF1<0的根，SKIPIF1<0是方程SKIPIF1<0的根，則SKIPIF1<0的值為（

）A．2 B．3 C．6 D．103．（2022·陜西·西安中學(xué)一模（理））函數(shù)SKIPIF1<0的所有零點(diǎn)之和為_(kāi)________.3.6零點(diǎn)定理（精練）（提升版）題組一題組一零點(diǎn)的區(qū)間1．（2022·甘肅·天水市第一中學(xué)）函數(shù)SKIPIF1<0的零點(diǎn)所在的區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02（2022·江蘇揚(yáng)州）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<03．（2022·天津紅橋·一模）函數(shù)SKIPIF1<0的零點(diǎn)所在的區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·廣東中山）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<05．（2022·北京師大附中）函數(shù)SKIPIF1<0的零點(diǎn)所在的區(qū)間是（

）A．（0，1） B．(1，2) C．(2，3) D．（3，4）6．（2022·云南玉溪·高一期末）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<07．（2022·寧夏·青銅峽市寧朔中學(xué)高二學(xué)業(yè)考試）函數(shù)SKIPIF1<0的零點(diǎn)所在的區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·新疆維吾爾自治區(qū)喀什第二中學(xué)）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<09．（2022·海南·嘉積中學(xué)高一期末）SKIPIF1<0零點(diǎn)所在的區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2022·四川·德陽(yáng)五中）函數(shù)SKIPIF1<0的零點(diǎn)所在的區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（2022·安徽·池州市第一中學(xué)）函數(shù)SKIPIF1<0的零點(diǎn)所在的一個(gè)區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2022·廣東汕尾）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題組二題組二零點(diǎn)的個(gè)數(shù)1．（2022·四川省瀘縣第二中學(xué)）函數(shù)SKIPIF1<0的零點(diǎn)的個(gè)數(shù)為（

）A．0 B．1 C．2 D．32．（2022·重慶）函數(shù)SKIPIF1<0的零點(diǎn)個(gè)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(gè)數(shù)為（

）A．0個(gè) B．1個(gè) C．2個(gè) D．3個(gè)4．（2022·新疆·三模（理））函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)為_(kāi)__________.5．（2022·新疆）函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)為_(kāi)________．題組三題組三比較零點(diǎn)的大小1．（2022·山西·二模（理））已知SKIPIF1<0是SKIPIF1<0的一個(gè)零點(diǎn)，SKIPIF1<0是SKIPIF1<0的一個(gè)零點(diǎn)，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022·湖南·益陽(yáng)市箴言中學(xué)）已知三個(gè)函數(shù)SKIPIF1<0的零點(diǎn)依次為SKIPIF1<0，則SKIPIF1<0的大小關(guān)系（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·陜西·長(zhǎng)安一中模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的零點(diǎn)分別為SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，則SKIPIF1<0、SKIPIF1<0、SKIPIF1<0的大小順序?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·安徽·蚌埠二中模擬預(yù)測(cè)（文））已知SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·河南河南·三模）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<0題組四題組四已知零點(diǎn)求參數(shù)1．（2022·湖北宜昌）函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0有兩個(gè)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<02．（2022·首都師范大學(xué)附屬中學(xué)）已知函數(shù)SKIPIF1<0，若SKIPIF1<0有三個(gè)不同的零點(diǎn)，則實(shí)數(shù)k的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·河北唐山）已知函數(shù)SKIPIF1<0，若SKIPIF1<0有3個(gè)零點(diǎn)，則a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·安徽）已知函數(shù)SKIPIF1<0在（0，+∞）上有3個(gè)不同的零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·江蘇泰州·模擬預(yù)測(cè)）已知定義在R上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，已知當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若SKIPIF1<0恰有六個(gè)不相等的零點(diǎn)，則實(shí)數(shù)m的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·內(nèi)蒙古·滿洲里市教研培訓(xùn)中心三模（文））已知函數(shù)SKIPIF1<0有唯一零點(diǎn)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知SKIPIF1<0是以2為周期的偶函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，那么在區(qū)間SKIPIF1<0內(nèi)，關(guān)于x的方程SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）有4個(gè)根，則k的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖象有兩個(gè)不同的交點(diǎn)，則實(shí)數(shù)m取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2022·天津·南開(kāi)中學(xué)模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0恰有兩個(gè)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<010．（2022·天津南開(kāi)·二模）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0若函數(shù)SKIPIF1<0恰有2個(gè)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<011．（2022·陜西·模擬預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0SKIPIF1<0在SKIPIF1<0上有且只有5個(gè)零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2022·陜西寶雞·二模（文））已知函數(shù)SKIPIF1<0（SKIPIF1<0是自然對(duì)數(shù)的底數(shù)）在定義域SKIPIF1<0上有三個(gè)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<013．（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上既有極大值又有極小值，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．（2022·河南·模擬預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0至多有2個(gè)不同的零點(diǎn)，則實(shí)數(shù)a的最大值為（

）．A．0 B．1 C．2 D．e15（2022·天津市武清區(qū)楊村第一中學(xué)二模）設(shè)SKIPIF1<0，函數(shù)SKIPIF1<0．若SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，且函數(shù)SKIPIF1<0與SKIPIF1<0的圖象有三個(gè)交點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．

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