3.6零點定理（精講）（提升版）思維導(dǎo)圖思維導(dǎo)圖考點呈現(xiàn)考點呈現(xiàn)例題剖析例題剖析考點一零點的區(qū)間【例1】（2022·河南開封·）函數(shù)SKIPIF1<0的一個零點所在的區(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考點二零點的個數(shù)【例2-1】（2022·陜西）函數(shù)SKIPIF1<0的零點個數(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)的零點個數(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的解的個數(shù)是（

）A．0 B．1 C．2 D．32．（2022·全國·高三專題練習(xí)）函數(shù)SKIPIF1<0的圖像與函數(shù)SKIPIF1<0的圖像的交點個數(shù)為（

）A．2 B．3 C．4 D．03．（2022·海南?。┰O(shè)函數(shù)SKIPIF1<0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，則函數(shù)SKIPIF1<0有（

）個零點A．4 B．5 C．6 D．7考點三比較零點的大小【例3】（2022·安徽）已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的零點分別為a，b，c則a，b，c的大小順序為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·河南）若實數(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）正實數(shù)SKIPIF1<0滿足SKIPIF1<0，則實數(shù)SKIPIF1<0之間的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點四已知零點求參數(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個不同的交點，則實數(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個不同實根，則實數(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個零點，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·高三專題練習(xí)）已知函數(shù)SKIPIF1<0若關(guān)于x的方程SKIPIF1<0恰有三個不相等的實數(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（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個零點，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·廣西·貴港市高級中學(xué)三模）已知SKIPIF1<0在SKIPIF1<0有且僅有6個實數(shù)根，則實數(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恰好有兩個零點，則實數(shù)k的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點五零點的綜合運用【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個零點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·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的零點為SKIPIF1<0，函數(shù)SKIPIF1<0的零點為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的一個零點，則SKIPIF1<0一定是下列哪個函數(shù)的零點（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0