新高考數(shù)學(xué)一輪復(fù)習(xí) 講與練第7講 函數(shù)與方程（原卷版）

第7講函數(shù)與方程學(xué)校____________姓名____________班級____________一、知識梳理1.函數(shù)的零點(diǎn)(1)概念：一般地，如果函數(shù)y＝f(x)在實數(shù)α處的函數(shù)值等于零，即f(α)＝0，則稱α為函數(shù)y＝f(x)的零點(diǎn).(2)函數(shù)的零點(diǎn)、函數(shù)的圖像與x軸的交點(diǎn)、對應(yīng)方程的根的關(guān)系：2.函數(shù)零點(diǎn)存在定理如果函數(shù)y＝f(x)在區(qū)間[a，b]上的圖像是連續(xù)不斷的，并且f(a)·f(b)<0(即在區(qū)間兩個端點(diǎn)處的函數(shù)值異號)，則函數(shù)y＝f(x)在區(qū)間(a，b)中至少有一個零點(diǎn)，即?x0∈(a，b)，f(x0)＝0.考點(diǎn)和典型例題1、函數(shù)零點(diǎn)所在區(qū)間的判斷【典例1-1】（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<0【典例1-2】（2021·山西·太原五中高三階段練習(xí)（文））利用二分法求方程SKIPIF1<0的近似解，可以取的一個區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例1-3】（2019·全國·高三專題練習(xí)）若SKIPIF1<0的一個正數(shù)零點(diǎn)附近的函數(shù)值用二分法逐次計算，數(shù)據(jù)如下表：SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0那么方程SKIPIF1<0的一個近似根（精確到0.1）為（

）A．1.2 B．1.3 C．1.4 D．1.5【典例1-4】（2022·天津·靜海一中高三階段練習(xí)）已知函數(shù)SKIPIF1<0是周期為SKIPIF1<0的周期函數(shù)，且當(dāng)時SKIPIF1<0時，SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)個數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例1-5】（2022·河南河南·三模（理））函數(shù)SKIPIF1<0的所有零點(diǎn)之和為（

）A．0 B．2 C．4 D．62、圖像零點(diǎn)個數(shù)的判定【典例2-1】（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【典例2-2】（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．6【典例2-3】（2016·天津市紅橋區(qū)教師發(fā)展中心高三學(xué)業(yè)考試）函數(shù)SKIPIF1<0．若在SKIPIF1<0內(nèi)恰有一個零點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2-4】（2022·湖南衡陽·二模）已知定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0恒有SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，已知SKIPIF1<0，則函數(shù)SKIPIF1<0在SKIPIF1<0上的零點(diǎn)個數(shù)為（

）A．4個 B．5個 C．3個或4個 D．4個或5個【典例2-5】（2022·寧夏銀川·一模（理））設(shè)函數(shù)SKIPIF1<0，已知SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0在SKIPIF1<0上的零點(diǎn)最多有（

）A．2個 B．3個 C．4個 D．5個3、圖像零點(diǎn)的綜合應(yīng)用【典例3-1】（2022·安徽·模擬預(yù)測（文））已知函數(shù)SKIPIF1<0，若SKIPIF1<0有4個零點(diǎn)，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例3-2】（2022·黑龍江·哈師大附中三模（文））已知有且只有一個實數(shù)x滿足SKIPIF1<0，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例3-3】（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<0【典例3-4】（2022·福建三明·模擬預(yù)測）已知函數(shù)SKIPIF1<0有兩個零點(diǎn)，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例3-5】（2022·山東濟(jì)寧·二模）已知函數(shù)SK