新高考數(shù)學(xué)二輪復(fù)習(xí)鞏固練習(xí)07 函數(shù)壓軸小題（原卷版）

鞏固練習(xí)07函數(shù)壓軸小題【秒殺總結(jié)】一、對(duì)于利用導(dǎo)數(shù)研究不等式的恒成立與有解問(wèn)題的求解策略：1、通常要構(gòu)造新函數(shù)，利用導(dǎo)數(shù)研究函數(shù)的單調(diào)性，求出最值，從而求出參數(shù)的取值范圍；2、利用可分離變量，構(gòu)造新函數(shù)，直接把問(wèn)題轉(zhuǎn)化為函數(shù)的最值問(wèn)題．3、根據(jù)恒成立求解參數(shù)的取值時(shí)，一般涉及分類(lèi)參數(shù)法，但壓軸試題中很少碰到分離參數(shù)后構(gòu)造的新函數(shù)能直接求出最值點(diǎn)的情況，通常要設(shè)出導(dǎo)數(shù)的零點(diǎn)，難度較大.二、對(duì)于雙變量問(wèn)題，首先變形后引入新變量把問(wèn)題變?yōu)閱巫兞?，再引入新函?shù)，利用導(dǎo)數(shù)求得函數(shù)值的范圍，然后再解相應(yīng)的不等式可得所求參數(shù)范圍．三、函數(shù)零點(diǎn)的求解與判斷方法：（1）直接求零點(diǎn)：令f(x)＝0，如果能求出解，則有幾個(gè)解就有幾個(gè)零點(diǎn)；（2）零點(diǎn)存在性定理：利用定理不僅要函數(shù)在區(qū)間[a，b]上是連續(xù)不斷的曲線(xiàn)，且f(a)·f(b)＜0，還必須結(jié)合函數(shù)的圖象與性質(zhì)(如單調(diào)性、奇偶性)才能確定函數(shù)有多少個(gè)零點(diǎn)；（3）利用圖象交點(diǎn)的個(gè)數(shù)：將函數(shù)變形為兩個(gè)函數(shù)的差，畫(huà)兩個(gè)函數(shù)的圖象，看其交點(diǎn)的橫坐標(biāo)有幾個(gè)不同的值，就有幾個(gè)不同的零點(diǎn).四、已知函數(shù)有零點(diǎn)(方程有根)求參數(shù)值(取值范圍)常用的方法：（1）直接法：直接求解方程得到方程的根，再通過(guò)解不等式確定參數(shù)范圍；（2）分離參數(shù)法：先將參數(shù)分離，轉(zhuǎn)化成求函數(shù)的值域問(wèn)題加以解決；（3）數(shù)形結(jié)合法：先對(duì)解析式變形，進(jìn)而構(gòu)造兩個(gè)函數(shù)，然后在同一平面直角坐標(biāo)系中畫(huà)出函數(shù)的圖像，利用數(shù)形結(jié)合的方法求解.【典型例題】例1．（2023春·廣東廣州·高三統(tǒng)考階段練習(xí)）已知函數(shù)SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0的定義域均R，若SKIPIF1<0為偶函數(shù)，且滿(mǎn)足SKIPIF1<0，則SKIPIF1<0（

）A．0 B．1 C．SKIPIF1<0 D．2例2．（2023秋·山東濰坊·高三統(tǒng)考期末）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿(mǎn)足SKIPIF1<0，對(duì)SKIPIF1<0，SKIPIF1<0，有SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例3．（2023·全國(guó)·模擬預(yù)測(cè)）下列大小關(guān)系正確的為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例4．（2023秋·江西撫州·高三臨川一中?？计谀┤艉瘮?shù)SKIPIF1<0的定義域?yàn)镽，且SKIPIF1<0偶函數(shù)，SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0成中心對(duì)稱(chēng)，則下列說(shuō)法正確的個(gè)數(shù)為（

）①SKIPIF1<0的一個(gè)周期為2；②SKIPIF1<0；③SKIPIF1<0的一個(gè)對(duì)稱(chēng)中心為SKIPIF1<0；④SKIPIF1<0.A．1 B．2 C．3 D．4例5．（多選題）（2023秋·河北石家莊·高三校聯(lián)考期末）已知函數(shù)SKIPIF1<0的定義域均為R，且SKIPIF1<0.若SKIPIF1<0的圖像關(guān)于直線(xiàn)SKIPIF1<0對(duì)稱(chēng)，且SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0對(duì)稱(chēng)C．SKIPIF1<0是周期函數(shù)，且最小正周期為8 D．SKIPIF1<0例6．（2023秋·山東濱州·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0（SKIPIF1<0為自然對(duì)數(shù)的底數(shù)），若關(guān)于SKIPIF1<0的方程SKIPIF1<0有且僅有四個(gè)不同的解，則實(shí)數(shù)SKIPIF1<0的取值范圍是_________．例7．（2023·全國(guó)·高三專(zhuān)題練習(xí)）已知函數(shù)SKIPIF1<0，若關(guān)于SKIPIF1<0的方程SKIPIF1<0有3個(gè)不同的實(shí)數(shù)根，則SKIPIF1<0的取值范圍為_(kāi)_____．例8．（2023·廣西梧州·統(tǒng)考一模）已知函數(shù)SKIPIF1<0，若關(guān)于x的方程SKIPIF1<0有5個(gè)不同的實(shí)數(shù)根，則a的取值范圍為_(kāi)______.例9．（2023·浙江省杭州第二中學(xué)高三開(kāi)學(xué)考試）已知函數(shù)SKIPIF1<0，有三個(gè)不同的零點(diǎn)，（其中SKIPIF1<0），則SKIPIF1<0的值為A．SKIPIF1<0 B．SKIPIF1<0 C．-1 D．1例10．（2023·全國(guó)·高二）若存在兩個(gè)正實(shí)數(shù)SKIPIF1<0、SKIPIF1<0，使得等式SKIPIF1<0成立，其中SKIPIF1<0為自然對(duì)數(shù)的底數(shù)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）．A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【過(guò)關(guān)測(cè)試】一、單選題1．（2023·黑龍江哈爾濱·高三哈爾濱三中?？茧A段練習(xí)）設(shè)SKIPIF1<0，則下列正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023·陜西渭南·統(tǒng)考一模）已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的定義域均為SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù).若SKIPIF1<0為偶函數(shù)，且SKIPIF1<0，SKIPIF1<0.則以下四個(gè)命題：①SKIPIF1<0；②SKIPIF1<0關(guān)于直線(xiàn)SKIPIF1<0對(duì)稱(chēng)；③SKIPIF1<0；④SKIPIF1<0中一定成立的是（

）A．①④ B．②③ C．①②③ D．①②④3．（2023·河南信陽(yáng)·高三統(tǒng)考期末）已知m、n為實(shí)數(shù)，SKIPIF1<0，若SKIPIF1<0對(duì)SKIPIF1<0恒成立，則SKIPIF1<0的最小值為（

）A．1 B．2 C．－1 D．34．（2023·遼寧·遼寧實(shí)驗(yàn)中學(xué)?？寄M預(yù)測(cè)）若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0、SKIPIF1<0、SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2023·江西吉安·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0的定義域均為SKIPIF1<0且都為連續(xù)函數(shù)，記SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0均為奇函數(shù)，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．2 D．20236．（2023·江蘇南通·高三統(tǒng)考期末）兩條曲線(xiàn)SKIPIF1<0與SKIPIF1<0存在兩個(gè)公共點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·江西新余·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0與SKIPIF1<0圖像的公共點(diǎn)個(gè)數(shù)為SKIPIF1<0，且這些公共點(diǎn)的橫坐標(biāo)從小到大依次為SKIPIF1<0，SKIPIF1<0，…，SKIPIF1<0，則下列說(shuō)法正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0B．若SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0D．若SKIPIF1<0，則SKIPIF1<08．（2023·全國(guó)·高三專(zhuān)題練習(xí)）設(shè)SKIPIF1<0是定義在SKIPIF1<0上且周期為4的奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，令SKIPIF1<0，則函數(shù)SKIPIF1<0的最大值為（

）A．1 B．SKIPIF1<0 C．2 D．SKIPIF1<09．（2023·全國(guó)·高三校聯(lián)考階段練習(xí)）定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿(mǎn)足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0有2023個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍可以是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2023·全國(guó)·高三專(zhuān)題練習(xí)）函數(shù)SKIPIF1<0滿(mǎn)足SKIPIF1<0，令SKIPIF1<0，對(duì)任意的SKIPIF1<0，都有SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．3 C．1 D．SKIPIF1<0二、多選題11．（2023·山東棗莊·高三統(tǒng)考期末）設(shè)定義在R上的函數(shù)SKIPIF1<0與SKIPIF1<0的導(dǎo)函數(shù)分別為SKIPIF1<0和SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0為奇函數(shù)，則（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于直線(xiàn)SKIPIF1<0對(duì)稱(chēng)B．函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱(chēng)C．SKIPIF1<0D．SKIPIF1<012．（2023·全國(guó)·高三專(zhuān)題練習(xí)）已知函數(shù)SKIPIF1<0和SKIPIF1<0，存在直線(xiàn)SKIPIF1<0與兩條曲線(xiàn)SKIPIF1<0和SKIPIF1<0共有三個(gè)不同的交點(diǎn)，并且從左到右的三個(gè)交點(diǎn)的橫坐標(biāo)分別為SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．（2023·遼寧·校聯(lián)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0、SKIPIF1<0的定義域均為SKIPIF1<0．且滿(mǎn)足SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱(chēng) D．SKIPIF1<014．（2023·江蘇南通·高三統(tǒng)考期末）設(shè)定義在SKIPIF1<0上的函數(shù)SKIPIF1<0與SKIPIF1<0的導(dǎo)數(shù)分別為SKIPIF1<0與SKIPIF1<0，已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0關(guān)于直線(xiàn)SKIPIF1<0對(duì)稱(chēng)，則下列結(jié)論一定成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<015．（2023·廣東清遠(yuǎn)·高三統(tǒng)考期末）設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．（2023·遼寧沈陽(yáng)·高三沈陽(yáng)二中?？计谀┮阎瘮?shù)SKIPIF1<0與SKIPIF1<0的定義域均為SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0為偶函數(shù)，則（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于直線(xiàn)SKIPIF1<0對(duì)稱(chēng) B．SKIPIF1<0C．函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱(chēng) D．SKIPIF1<0三、填空題17．（2023·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恰有兩個(gè)不相等的實(shí)數(shù)根SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的取值范圍是______．18．（2023·湖南長(zhǎng)沙·高三長(zhǎng)沙一中?？茧A段練習(xí)）已知定義在SKIPIF1<0上的單調(diào)遞增函數(shù)SKIPIF1<0，對(duì)于任意的SKIPIF1<0，都有SKIPIF1<0，且SKIPIF1<0恒成立，則SKIPIF1<0______.19．（2023·江西·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0，SKIPI