新高考數(shù)學(xué)二輪復(fù)習(xí)精講精練專題16 函數(shù)與導(dǎo)數(shù)常見(jiàn)經(jīng)典壓軸小題全歸類（原卷版）

專題16函數(shù)與導(dǎo)數(shù)常見(jiàn)經(jīng)典壓軸小題全歸類【命題規(guī)律】1、導(dǎo)數(shù)的計(jì)算和幾何意義是高考命題的熱點(diǎn)，多以選擇題、填空題形式考查，難度較小．2、應(yīng)用導(dǎo)數(shù)研究函數(shù)的單調(diào)性、極值、最值多在選擇題、填空題靠后的位置考查，難度中等偏上，屬綜合性問(wèn)題．【核心考點(diǎn)目錄】核心考點(diǎn)一：函數(shù)零點(diǎn)問(wèn)題之分段分析法模型核心考點(diǎn)二：函數(shù)嵌套問(wèn)題核心考點(diǎn)三：函數(shù)整數(shù)解問(wèn)題核心考點(diǎn)四：唯一零點(diǎn)求值問(wèn)題核心考點(diǎn)五：等高線問(wèn)題核心考點(diǎn)六：分段函數(shù)零點(diǎn)問(wèn)題核心考點(diǎn)七：函數(shù)對(duì)稱問(wèn)題核心考點(diǎn)八：零點(diǎn)嵌套問(wèn)題核心考點(diǎn)九：函數(shù)零點(diǎn)問(wèn)題之三變量問(wèn)題核心考點(diǎn)十：倍值函數(shù)核心考點(diǎn)十一：函數(shù)不動(dòng)點(diǎn)問(wèn)題核心考點(diǎn)十二：函數(shù)的旋轉(zhuǎn)問(wèn)題核心考點(diǎn)十三：構(gòu)造函數(shù)解不等式核心考點(diǎn)十四：導(dǎo)數(shù)中的距離問(wèn)題核心考點(diǎn)十五：導(dǎo)數(shù)的同構(gòu)思想核心考點(diǎn)十六：不等式恒成立之分離參數(shù)、分離函數(shù)、放縮法核心考點(diǎn)十七：三次函數(shù)問(wèn)題核心考點(diǎn)十八：切線問(wèn)題核心考點(diǎn)十九：任意存在性問(wèn)題核心考點(diǎn)二十：雙參數(shù)最值問(wèn)題核心考點(diǎn)二十一：切線斜率與割線斜率核心考點(diǎn)二十二：最大值的最小值問(wèn)題（平口單峰函數(shù)、鉛錘距離）核心考點(diǎn)二十三：兩邊夾問(wèn)題和零點(diǎn)相同問(wèn)題核心考點(diǎn)二十四：函數(shù)的伸縮變換問(wèn)題【真題回歸】1．（2022·全國(guó)·統(tǒng)考高考真題）當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0取得最大值SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．12．（2022·全國(guó)·統(tǒng)考高考真題）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0的最小值、最大值分別為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（多選題）（2022·全國(guó)·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0有兩個(gè)極值點(diǎn) B．SKIPIF1<0有三個(gè)零點(diǎn)C．點(diǎn)SKIPIF1<0是曲線SKIPIF1<0的對(duì)稱中心 D．直線SKIPIF1<0是曲線SKIPIF1<0的切線4．（2022·天津·統(tǒng)考高考真題）設(shè)SKIPIF1<0，對(duì)任意實(shí)數(shù)x，記SKIPIF1<0．若SKIPIF1<0至少有3個(gè)零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍為_(kāi)_____.5．（2022·全國(guó)·統(tǒng)考高考真題）已知SKIPIF1<0和SKIPIF1<0分別是函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的極小值點(diǎn)和極大值點(diǎn)．若SKIPIF1<0，則a的取值范圍是____________．6．（2022·全國(guó)·統(tǒng)考高考真題）若曲線SKIPIF1<0有兩條過(guò)坐標(biāo)原點(diǎn)的切線，則a的取值范圍是________________．7．（2022·浙江·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0則SKIPIF1<0________；若當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0的最大值是_________．8．（2022·全國(guó)·統(tǒng)考高考真題）曲線SKIPIF1<0過(guò)坐標(biāo)原點(diǎn)的兩條切線的方程為_(kāi)___________，____________．9．（2022·北京·統(tǒng)考高考真題）設(shè)函數(shù)SKIPIF1<0若SKIPIF1<0存在最小值，則a的一個(gè)取值為_(kāi)_______；a的最大值為_(kāi)__________．【方法技巧與總結(jié)】1、求分段函數(shù)的函數(shù)值，要先確定要求值的自變量屬于哪一段區(qū)間，然后代入該段的解析式求值，當(dāng)出現(xiàn)SKIPIF1<0的形式時(shí)，應(yīng)從內(nèi)到外依次求值；當(dāng)給出函數(shù)值求自變量的值時(shí)，先假設(shè)所求的值在分段函數(shù)定義區(qū)間的各段上，然后求出相應(yīng)自變量的值，切記要代入檢驗(yàn)，看所求的自變量的值是否滿足相應(yīng)段自變量的取值范圍．2、含有抽象函數(shù)的分段函數(shù)，在處理時(shí)首先要明確目標(biāo)，即讓自變量向有具體解析式的部分靠攏，其次要理解抽象函數(shù)的含義和作用（或者對(duì)函數(shù)圖象的影響）．3、含分段函數(shù)的不等式在處理上通常有兩種方法：一種是利用代數(shù)手段，通過(guò)對(duì)SKIPIF1<0進(jìn)行分類討論將不等式轉(zhuǎn)變?yōu)榫唧w的不等式求解；另一種是通過(guò)作出分段函數(shù)的圖象，數(shù)形結(jié)合，利用圖象的特點(diǎn)解不等式．4、分段函數(shù)零點(diǎn)的求解與判斷方法：（1）直接法：直接根據(jù)題設(shè)條件構(gòu)造關(guān)于參數(shù)的不等式，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)化成球函數(shù)值域的問(wèn)題加以解決；（3）數(shù)形結(jié)合法：先將解析式變形，在同一平面直角坐標(biāo)系中，畫(huà)出函數(shù)的圖象，然后數(shù)形結(jié)合求解．5、動(dòng)態(tài)二次函數(shù)中靜態(tài)的值：解決這類問(wèn)題主要考慮二次函數(shù)的有關(guān)性質(zhì)及式子變形，注意二次函數(shù)的系數(shù)、圖象的開(kāi)口、對(duì)稱軸是否存在不變的性質(zhì)，二次函數(shù)的圖象是否過(guò)定點(diǎn)，從而簡(jiǎn)化解題．6、動(dòng)態(tài)二次函數(shù)零點(diǎn)個(gè)數(shù)和分布問(wèn)題：通常轉(zhuǎn)化為相應(yīng)二次函數(shù)的圖象與SKIPIF1<0軸交點(diǎn)的個(gè)數(shù)問(wèn)題，結(jié)合二次函數(shù)的圖象，通過(guò)對(duì)稱軸，根的判別式，相應(yīng)區(qū)間端點(diǎn)函數(shù)值等來(lái)考慮．7、求二次函數(shù)最值問(wèn)題，應(yīng)結(jié)合二次函數(shù)的圖象求解，有三種常見(jiàn)類型：（1）對(duì)稱軸變動(dòng)，區(qū)間固定；（2）對(duì)稱軸固定，區(qū)間變動(dòng)；（3）對(duì)稱軸變動(dòng)，區(qū)間也變動(dòng)．這時(shí)要討論對(duì)稱軸何時(shí)在區(qū)間之內(nèi)，何時(shí)在區(qū)間之外．討論的目的是確定對(duì)稱軸和區(qū)間的關(guān)系，明確函數(shù)的單調(diào)情況，從而確定函數(shù)的最值．8、由于三次函數(shù)的導(dǎo)函數(shù)為我們最熟悉的二次函數(shù)，所以基本的研究思路是：借助導(dǎo)函數(shù)的圖象來(lái)研究原函數(shù)的圖象．如借助導(dǎo)函數(shù)的正負(fù)研究原函數(shù)的單調(diào)性；借助導(dǎo)函數(shù)的（變號(hào)）零點(diǎn)研究原函數(shù)的極值點(diǎn)（最值點(diǎn)）；綜合借助導(dǎo)函數(shù)的圖象畫(huà)出原函數(shù)的圖象并研究原函數(shù)的零點(diǎn)…具體來(lái)說(shuō)，對(duì)于三次函數(shù)SKIPIF1<0，其導(dǎo)函數(shù)為SKIPIF1<0，根的判別式SKIPIF1<0．SKIPIF1<0SKIPIF1<0判別式SKIPIF1<0SKIPIF1<0SKIPIF1<0圖象SKIPIF1<0單調(diào)性增區(qū)間：SKIPIF1<0，SKIPIF1<0；減區(qū)間：SKIPIF1<0增區(qū)間：SKIPIF1<0增區(qū)間：SKIPIF1<0圖象（1）當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0恒成立，三次函數(shù)SKIPIF1<0在SKIPIF1<0上為增函數(shù)，沒(méi)有極值點(diǎn)，有且只有一個(gè)零點(diǎn)；（2）當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0有兩根SKIPIF1<0，SKIPIF1<0，不妨設(shè)SKIPIF1<0，則SKIPIF1<0，可得三次函數(shù)SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上為增函數(shù)，在SKIPIF1<0上為減函數(shù)，則SKIPIF1<0，SKIPIF1<0分別為三次函數(shù)SKIPIF1<0的兩個(gè)不相等的極值點(diǎn)，那么：①若SKIPIF1<0，則SKIPIF1<0有且只有SKIPIF1<0個(gè)零點(diǎn)；②若SKIPIF1<0，則SKIPIF1<0有SKIPIF1<0個(gè)零點(diǎn)；③若SKIPIF1<0，則SKIPIF1<0有SKIPIF1<0個(gè)零點(diǎn)．特別地，若三次函數(shù)SKIPIF1<0存在極值點(diǎn)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0地解析式為SKIPIF1<0．同理，對(duì)于三次函數(shù)SKIPIF1<0，其性質(zhì)也可類比得到．9、由于三次函數(shù)SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0為二次函數(shù)，其圖象變化規(guī)律具有對(duì)稱性，所以三次函數(shù)圖象也應(yīng)當(dāng)具有對(duì)稱性，其圖象對(duì)稱中心應(yīng)當(dāng)為點(diǎn)SKIPIF1<0，此結(jié)論可以由對(duì)稱性的定義加以證明．事實(shí)上，該圖象對(duì)稱中心的橫坐標(biāo)正是三次函數(shù)導(dǎo)函數(shù)的極值點(diǎn)．10、對(duì)于三次函數(shù)圖象的切線問(wèn)題，和一般函數(shù)的研究方法相同．導(dǎo)數(shù)的幾何意義就是求圖象在該店處切線的斜率，利用導(dǎo)數(shù)研究函數(shù)的切線問(wèn)題，要區(qū)分“在”與“過(guò)”的不同，如果是過(guò)某一點(diǎn)，一定要設(shè)切點(diǎn)坐標(biāo)，然后根據(jù)具體的條件得到方程，然后解出參數(shù)即可．11、恒成立（或存在性）問(wèn)題常常運(yùn)用分離參數(shù)法，轉(zhuǎn)化為求具體函數(shù)的最值問(wèn)題．12、如果無(wú)法分離參數(shù)，可以考慮對(duì)參數(shù)或自變量進(jìn)行分類討論，利用函數(shù)性質(zhì)求解，常見(jiàn)的是利用函數(shù)單調(diào)性求解函數(shù)的最大、最小值．13、當(dāng)不能用分離參數(shù)法或借助于分類討論解決問(wèn)題時(shí)，還可以考慮利用函數(shù)圖象來(lái)求解，即利用數(shù)形結(jié)合思想解決恒成立（或存在性）問(wèn)題，此時(shí)應(yīng)先構(gòu)造函數(shù)，作出符合已知條件的圖形，再考慮在給定區(qū)間上函數(shù)圖象之間的關(guān)系，得出答案或列出條件，求出參數(shù)的范圍．14、兩類零點(diǎn)問(wèn)題的不同處理方法利用零點(diǎn)存在性定理的條件為函數(shù)圖象在區(qū)間[a，b]上是連續(xù)不斷的曲線，且SKIPIF1<0．．①直接法：判斷-一個(gè)零點(diǎn)時(shí)，若函數(shù)為單調(diào)函數(shù)，則只需取值證明SKIPIF1<0．②分類討論法：判斷幾個(gè)零點(diǎn)時(shí)，需要先結(jié)合單調(diào)性，確定分類討論的標(biāo)準(zhǔn)，再利用零點(diǎn)存在性定理，在每個(gè)單調(diào)區(qū)間內(nèi)取值證明SKIPIF1<0．15、利用導(dǎo)數(shù)研究方程根（函數(shù)零點(diǎn)）的技巧（1）研究方程根的情況，可以通過(guò)導(dǎo)數(shù)研究函數(shù)的單調(diào)性、最大值、最小值、變化趨勢(shì)等．（2）根據(jù)題目要求，畫(huà)出函數(shù)圖象的走勢(shì)規(guī)律，標(biāo)明函數(shù)極（最）值的位置．（3）利用數(shù)形結(jié)合的思想去分析問(wèn)題，可以使問(wèn)題的求解有一個(gè)清晰、直觀的整體展現(xiàn)．16、已知函數(shù)零點(diǎn)個(gè)數(shù)求參數(shù)的常用方法（1）分離參數(shù)法：首先分離出參數(shù)，然后利用求導(dǎo)的方法求出構(gòu)造的新函數(shù)的最值，根據(jù)題設(shè)條件構(gòu)建關(guān)于參數(shù)的不等式，再通過(guò)解不等式確定參數(shù)范圍．（2）分類討論法：結(jié)合單調(diào)性，先確定參數(shù)分類的標(biāo)準(zhǔn)，在每個(gè)小范圍內(nèi)研究零點(diǎn)的個(gè)數(shù)是否符合題意，將滿足題意的參數(shù)的各小范圍并在一起，即為所求參數(shù)范圍．【核心考點(diǎn)】核心考點(diǎn)一：函數(shù)零點(diǎn)問(wèn)題之分段分析法模型【典型例題】例1．（2023·浙江奉化·高二期末）若函數(shù)SKIPIF1<0至少存在一個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例2．（2023·天津·耀華中學(xué)高二期中）設(shè)函數(shù)SKIPIF1<0，記SKIPIF1<0，若函數(shù)SKIPIF1<0至少存在一個(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<0例3．（2023·湖南·長(zhǎng)沙一中高三月考（文））設(shè)函數(shù)SKIPIF1<0（其中SKIPIF1<0為自然對(duì)數(shù)的底數(shù)），若函數(shù)SKIPIF1<0至少存在一個(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<0核心考點(diǎn)二：函數(shù)嵌套問(wèn)題【典型例題】例4．（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，設(shè)關(guān)于SKIPIF1<0的方程SKIPIF1<0有SKIPIF1<0個(gè)不同的實(shí)數(shù)解，則SKIPIF1<0的所有可能的值為A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<0或SKIPIF1<0例5．（2023·全國(guó)·高三專題練習(xí)（文））已知函數(shù)SKIPIF1<0，SKIPIF1<0若關(guān)于x的方程SKIPIF1<0有四個(gè)不同的解，則實(shí)數(shù)m的取值集合為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例6．（2023·河南·高三月考（文））已知函數(shù)SKIPIF1<0，若關(guān)于SKIPIF1<0的方程SKIPIF1<0有且僅有三個(gè)不同的實(shí)數(shù)解，則實(shí)數(shù)SKIPIF1<0的取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)三：函數(shù)整數(shù)解問(wèn)題【典型例題】例7．（2023·福建寧德·高三）當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0恒成立，則整數(shù)SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例8．（2023·江蘇·蘇州大學(xué)附屬中學(xué)高三月考）已知SKIPIF1<0，關(guān)于x的一元二次不等式SKIPIF1<0的解集中有且僅有3個(gè)整數(shù)，則所有符合條件的a的值之和是（）A．13 B．21 C．26 D．30例9．（2023·江蘇宿遷·高一月考）用符號(hào)[x]表示不超過(guò)x的最大整數(shù)（稱為x的整數(shù)部分），如[﹣1.2]=﹣2，[0.2]=0，[1]=1，設(shè)函數(shù)f（x）=（1﹣lnx）（lnx﹣ax）有三個(gè)不同的零點(diǎn)x1，x2，x3，若[x1]+[x2]+[x3]=6，則實(shí)數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)四：唯一零點(diǎn)求值問(wèn)題【典型例題】例10．（2023·安徽蚌埠·模擬預(yù)測(cè)（理））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<0例11．（2023·遼寧沈陽(yáng)·模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0分別是定義在SKIPIF1<0上的偶函數(shù)和奇函數(shù)，且SKIPIF1<0，若函數(shù)SKIPIF1<0有唯一零點(diǎn)，則正實(shí)數(shù)SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例12．（2023·新疆·莎車縣第一中學(xué)高三期中）已知函數(shù)SKIPIF1<0，SKIPIF1<0分別是定義在SKIPIF1<0上的偶函數(shù)和奇函數(shù)，且SKIPIF1<0，若函數(shù)SKIPIF1<0有唯一零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的值為A．SKIPIF1<0或SKIPIF1<0 B．1或SKIPIF1<0 C．SKIPIF1<0或2 D．SKIPIF1<0或1核心考點(diǎn)五：等高線問(wèn)題【典型例題】例13．（2023·陜西·千陽(yáng)縣中學(xué)模擬預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0SKIPIF1<0的SKIPIF1<0個(gè)不同實(shí)根從小到大依次為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，有以下三個(gè)結(jié)論：①SKIPIF1<0且SKIPIF1<0；②當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0且SKIPIF1<0；③SKIPIF1<0．其中正確的結(jié)論個(gè)數(shù)為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例14．（2023·江蘇省天一中學(xué)高三月考）已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0有3個(gè)不同的實(shí)根SKIPIF1<0，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例15．（2023·浙江·高一單元測(cè)試）已知函數(shù)SKIPIF1<0，其中SKIPIF1<0，若方程SKIPIF1<0有四個(gè)不同的實(shí)根SKIPIF1<0、SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)六：分段函數(shù)零點(diǎn)問(wèn)題【典型例題】例16．（2023·山東青島·高三期末）已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0有4個(gè)不相同的解，則實(shí)數(shù)m的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例17．（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，SKIPIF1<0，若函數(shù)SKIPIF1<0有兩個(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例18．（2023·江蘇·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0，若SKIPIF1<0有兩個(gè)零點(diǎn)，則m的取值范圍是（）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)七：函數(shù)對(duì)稱問(wèn)題【典型例題】例19．（2023·安徽省滁州中學(xué)高三月考（文））已知函數(shù)SKIPIF1<0的圖象上有且僅有四個(gè)不同的點(diǎn)關(guān)于直線SKIPIF1<0的對(duì)稱點(diǎn)在SKIPIF1<0的圖象上,則實(shí)數(shù)SKIPIF1<0的取值范圍是A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例20．（2023·全國(guó)·高一課時(shí)練習(xí)）若直角坐標(biāo)平面內(nèi)的兩點(diǎn)P，Q滿足條件：①P，Q都在函數(shù)SKIPIF1<0的圖象上；②P，Q關(guān)于原點(diǎn)對(duì)稱，則稱點(diǎn)對(duì)SKIPIF1<0是函數(shù)SKIPIF1<0的一個(gè)“友好點(diǎn)對(duì)”（注：點(diǎn)對(duì)SKIPIF1<0與SKIPIF1<0看作同一個(gè)“友好點(diǎn)對(duì)”）．已知函數(shù)SKIPIF1<0，則此函數(shù)的“友好點(diǎn)對(duì)”有（）A．0個(gè) B．1個(gè) C．2個(gè) D．3個(gè)例21．（2023·福建·廈門(mén)一中高一競(jìng)賽）若函數(shù)y＝f(x)圖象上存在不同的兩點(diǎn)A，B關(guān)于y軸對(duì)稱，則稱點(diǎn)對(duì)[A，B]是函數(shù)y＝f(x)的一對(duì)“黃金點(diǎn)對(duì)”（注：點(diǎn)對(duì)[A，B]與[B，A]可看作同一對(duì)“黃金點(diǎn)對(duì)”）已知函數(shù)SKIPIF1<0，則此函數(shù)的“黃金點(diǎn)對(duì)”有（）A．0對(duì) B．1對(duì) C．2對(duì) D．3對(duì)核心考點(diǎn)八：零點(diǎn)嵌套問(wèn)題【典型例題】例22．（2023·湖北武漢·高三月考）已知函數(shù)SKIPIF1<0有三個(gè)不同的零點(diǎn)SKIPIF1<0.其中SKIPIF1<0，則SKIPIF1<0的值為（）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例23．（2023·全國(guó)·模擬預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0有三個(gè)不同的零點(diǎn)SKIPIF1<0（其中SKIPIF1<0），則SKIPIF1<0的值為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例24．（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核心考點(diǎn)九：函數(shù)零點(diǎn)問(wèn)題之三變量問(wèn)題【典型例題】例25．（2023·全國(guó)·高三）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例26．（2023·山東棗莊·高二期末）對(duì)于任意的實(shí)數(shù)SKIPIF1<0，總存在三個(gè)不同的實(shí)數(shù)SKIPIF1<0，使得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<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例27．（2023·四川省新津中學(xué)高三月考（理））若存在兩個(gè)正實(shí)數(shù)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的取值范圍為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)十：倍值函數(shù)【典型例題】例28．（河南省鄭州市第一中學(xué)2022-2023學(xué)年高三上學(xué)期期中考試數(shù)學(xué)（理）試題）對(duì)于函數(shù)SKIPIF1<0，若存在區(qū)間SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)的值域?yàn)镾KIPIF1<0，則稱SKIPIF1<0為SKIPIF1<0倍值函數(shù).若SKIPIF1<0是SKIPIF1<0倍值函數(shù)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例29．（2023·四川·內(nèi)江市教育科學(xué)研究所高二期末（文））對(duì)于函數(shù)SKIPIF1<0，若存在區(qū)間SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的值域?yàn)镾KIPIF1<0，則稱SKIPIF1<0為SKIPIF1<0倍值函數(shù).若SKIPIF1<0是SKIPIF1<0倍值函數(shù)，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例30．（2023·吉林·長(zhǎng)春十一高高二期中（理））對(duì)于函數(shù)SKIPIF1<0，若存在區(qū)間SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的值域?yàn)镾KIPIF1<0，則稱SKIPIF1<0為SKIPIF1<0倍值函數(shù)．若SKIPIF1<0是SKIPIF1<0倍值函數(shù)，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)十一：函數(shù)不動(dòng)點(diǎn)問(wèn)題【典型例題】例31．（2023·廣東海珠·高三期末）設(shè)函數(shù)SKIPIF1<0（SKIPIF1<0為自然對(duì)數(shù)的底數(shù)），若曲線SKIPIF1<0上存在點(diǎn)SKIPIF1<0使得SKIPIF1<0，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例32．（2023·山西省榆社中學(xué)高三月考（理））若存在一個(gè)實(shí)數(shù)t，使得SKIPIF1<0成立，則稱t為函數(shù)SKIPIF1<0的一個(gè)不動(dòng)點(diǎn).設(shè)函數(shù)SKIPIF1<0(SKIPIF1<0，e為自然對(duì)數(shù)的底數(shù))，定義在R上的連續(xù)函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.若存在SKIPIF1<0，且SKIPIF1<0為函數(shù)SKIPIF1<0的一個(gè)不動(dòng)點(diǎn)，則實(shí)數(shù)a的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例33．（2023·四川自貢·高二期末（文））設(shè)函數(shù)SKIPIF1<0，若存在SKIPIF1<0(SKIPIF1<0為自然對(duì)數(shù)的底數(shù))，使得SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)十二：函數(shù)的旋轉(zhuǎn)問(wèn)題【典型例題】例34．（2023·上海市建平中學(xué)高三期末）雙曲線SKIPIF1<0繞坐標(biāo)原點(diǎn)O旋轉(zhuǎn)適當(dāng)角度可以成為函數(shù)f（x）的圖象，關(guān)于此函數(shù)f（x）有如下四個(gè)命題，其中真命題的個(gè)數(shù)為（）①f（x）是奇函數(shù)；②f（x）的圖象過(guò)點(diǎn)SKIPIF1<0或SKIPIF1<0；③f（x）的值域是SKIPIF1<0；④函數(shù)y＝f（x）－x有兩個(gè)零點(diǎn)．A．4個(gè) B．3個(gè) C．2個(gè) D．1個(gè)例35．（2023·山東青島·高三開(kāi)學(xué)考試）將函數(shù)SKIPIF1<0的圖象繞點(diǎn)SKIPIF1<0逆時(shí)針旋轉(zhuǎn)SKIPIF1<0，得到曲線SKIPIF1<0，對(duì)于每一個(gè)旋轉(zhuǎn)角SKIPIF1<0，曲線SKIPIF1<0都是一個(gè)函數(shù)的圖象，則SKIPIF1<0最大時(shí)的正切值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例36．（2023·浙江·高三期末）將函數(shù)SKIPIF1<0的圖像繞著原點(diǎn)逆時(shí)針旋轉(zhuǎn)角SKIPIF1<0得到曲線SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)都能使SKIPIF1<0成為某個(gè)函數(shù)的圖像，則SKIPIF1<0的最大值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)十三：構(gòu)造函數(shù)解不等式【典型例題】例37．（2023·江西贛州·高三期中（文））已知函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0的導(dǎo)數(shù)SKIPIF1<0，則不等式SKIPIF1<0的解集為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例38．（2023·全國(guó)·高二課時(shí)練習(xí)）設(shè)定義在SKIPIF1<0上的函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則不等式SKIPIF1<0（其中SKIPIF1<0為自然對(duì)數(shù)的底數(shù)）的解集為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例39．（2023·全國(guó)·高二課時(shí)練習(xí)）已知SKIPIF1<0的定義域?yàn)镾KIPIF1<0，SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)，且滿足SKIPIF1<0，則不等式SKIPIF1<0的解集是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)十四：導(dǎo)數(shù)中的距離問(wèn)題【典型例題】例40．（2023春?荔灣區(qū)期末）設(shè)函數(shù)SKIPIF1<0，其中SKIPIF1<0，SKIPIF1<0，存在SKIPIF1<0使得SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的值是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．1例41．（2023?龍巖模擬）若對(duì)任意的正實(shí)數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0在SKIPIF1<0上都是增函數(shù)，則實(shí)數(shù)SKIPIF1<0的取值范圍是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<0例42．（2023?淮北一模）若存在實(shí)數(shù)SKIPIF1<0使得關(guān)于SKIPIF1<0的不等式SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<0核心考點(diǎn)十五：導(dǎo)數(shù)的同構(gòu)思想【典型例題】例43．（2023·全國(guó)·高三專題練習(xí)）已知關(guān)于SKIPIF1<0的不等式SKIPIF1<0在SKIPIF1<0恒成立，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例44．（2023·安徽·合肥一中高三月考（理））設(shè)實(shí)數(shù)SKIPIF1<0，若對(duì)任意的SKIPIF1<0，不等式SKIPIF1<0恒成立，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45．（2023·寧夏·石嘴山市第一中學(xué)高二月考（理））若對(duì)任意SKIPIF1<0，不等式SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)十六：不等式恒成立之分離參數(shù)、分離函數(shù)、放縮法【典型例題】例46．（2023·浙江·高三月考）已知函數(shù)SKIPIF1<0，不等式SKIPIF1<0對(duì)任意SKIPIF1<0恒成立，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47．（2023·四川省資中縣第二中學(xué)高二月考（理））關(guān)于SKIPIF1<0的不等式SKIPIF1<0對(duì)任意SKIPIF1<0恒成立，則SKIPIF1<0的取值范圍是（）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例48．（2023·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0，若關(guān)于SKIPIF1<0的不等式SKIPIF1<0恒成立，則SKIPIF1<0的最大值為_(kāi)______．核心考點(diǎn)十七：三次函數(shù)問(wèn)題【典型例題】例49．（2023·全國(guó)·高三課時(shí)練習(xí)）設(shè)函數(shù)SKIPIF1<0是SKIPIF1<0的導(dǎo)數(shù)，經(jīng)過(guò)探究發(fā)現(xiàn)，任意一個(gè)三次函數(shù)SKIPIF1<0的圖象都有對(duì)稱中心SKIPIF1<0，其中SKIPIF1<0滿足SKIPIF1<0，已知函數(shù)SKIPIF1<0，則SKIPIF1<0（）A．2021 B．SKIPIF1<0 C．2022 D．SKIPIF1<0例50．（2023·安徽·東至縣第二中學(xué)高三月考（理））人們?cè)谘芯繉W(xué)習(xí)過(guò)程中，發(fā)現(xiàn)：三次整式函數(shù)SKIPIF1<0都有對(duì)稱中心，其對(duì)稱中心為SKIPIF1<0（其中SKIPIF1<0）.已知函數(shù)SKIPIF1<0.若SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例51．（2023·全國(guó)·高三月考（文））已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，若三次函數(shù)SKIPIF1<0有三個(gè)零點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，且滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)十八：切線問(wèn)題【典型例題】例52．（2023·云南紅河·高三月考（理））下列關(guān)于三次函數(shù)SKIPIF1<0敘述正確的是（）①函數(shù)SKIPIF1<0的圖象一定是中心對(duì)稱圖形；②函數(shù)SKIPIF1<0可能只有一個(gè)極值點(diǎn)；③當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0處的切線與函數(shù)SKIPIF1<0的圖象有且僅有兩個(gè)交點(diǎn)；④當(dāng)SKIPIF1<0時(shí)，則過(guò)點(diǎn)SKIPIF1<0的切線可能有一條或者三條．A．①③ B．②③ C．①④ D．②④例53．（2023·江西·南昌二中高三月考（文））若函數(shù)SKIPIF1<0的圖象與曲線C:SKIPIF1<0存在公共切線，則實(shí)數(shù)SKIPIF1<0的取值范圍為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例54．（2023·全國(guó)·高二單元測(cè)試）若過(guò)點(diǎn)SKIPIF1<0可以作曲線SKIPIF1<0的兩條切線，則()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)十九：任意存在性問(wèn)題【典型例題】例55．（2023·河南·鄭州外國(guó)語(yǔ)中學(xué)高三月考（理））若不等式SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0.例56．（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0對(duì)SKIPIF1<0，總有SKIPIF1<0，使SKIPIF1<0成立，則SKIPIF1<0的范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例57．（2023·全國(guó)·高二課時(shí)練習(xí)）已知SKIPIF1<0，若SKIPIF1<0，且SKIPIF1<0對(duì)任意SKIPIF1<0恒成立，則k的最大值為（）A．3 B．4 C．5 D．6核心考點(diǎn)二十：雙參數(shù)最值問(wèn)題【典型例題】例58．（2023·浙江·寧波市北侖中學(xué)高三開(kāi)學(xué)考試）已知SKIPIF1<0，且SKIPIF1<0，對(duì)任意SKIPIF1<0均有SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例59．（2023·山西運(yùn)城·高三期中（理））已知在函數(shù)SKIPIF1<0，SKIPIF1<0，若對(duì)SKIPIF1<0，SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例60．（2023·黑龍江·鶴崗一中高三月考（理））當(dāng)SKIPIF1<0時(shí)，不等式SKIPIF1<0，SKIPIF1<0，SKIPIF1<0恒成立，則SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)二十一：切線斜率與割線斜率【典型例題】例61．（2023·廣東·佛山一中高三月考）已知函數(shù)SKIPIF1<0SKIPIF1<0，在函數(shù)SKIPIF1<0圖象上任取兩點(diǎn)SKIPIF1<0，若直線SKIPIF1<0的斜率的絕對(duì)值都不小于SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例62．（2023·山西大同·高一期中）已知函數(shù)SKIPIF1<0是定義在R上的函數(shù)，且SKIPIF1<0是奇函數(shù)，SKIPIF1<0是偶函數(shù)，SKIPIF1<0SKIPIF1<0，記SKIPIF1<0，若對(duì)于任意的SKIPIF1<0，都有SKIPIF1<0，則實(shí)數(shù)a的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例63．（2023·全國(guó)·高一課時(shí)練習(xí)）已知函數(shù)SKIPIF1<0，若對(duì)任意的SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0成立，則實(shí)數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0核心考點(diǎn)二十二：最大值的最小值問(wèn)題（平口單峰函數(shù)、鉛錘距離）【典型例題】例64．設(shè)二次函數(shù)SKIPIF1<0在SKIPIF1<0上有最大值，最大值為SKIPIF1<0（a），當(dāng)SKIPIF1<0（a）取最小值時(shí)，SKIPIF1<0SKIPIF1<0A．0 B．1 C．SKIPIF1<0 D．SKIPIF1<0例65．（2023春?紹興期末）已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，設(shè)SKIPIF1<0的最大值為SKIPIF1<0，若SKIPIF1<0的最小值為1時(shí)，則SKIPIF1<0的值可以是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．0 C．SKIPIF1<0 D．1例66．（2023?濟(jì)南模擬）已知函數(shù)SKIPIF1<0，若對(duì)任意的實(shí)數(shù)SKIPIF1<0，SKIPIF1<0，總存在SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<0核心考點(diǎn)二十三：兩邊夾問(wèn)題和零點(diǎn)相同問(wèn)題【典型例題】例67．（2023春?湖州期末）若存在正實(shí)數(shù)SKIPIF1<0，SKIPIF1<0使得不等式SKIPIF1<0成立，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例68．（2023?上饒二模）已知實(shí)數(shù)SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的值為SKIPIF1<0SKIPIF1<0A．2 B．1 C．0 D．SKIPIF1<0例69．（2023?崇明區(qū)期末）若不等式SKIPIF1<0對(duì)SKIPIF1<0，SKIPIF1<0恒成立，則SKIPIF1<0的值等于SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．2核心考點(diǎn)二十四：函數(shù)的伸縮變換問(wèn)題【典型例題】例70．（2023·天津一中高三月考）定義域?yàn)镾KIPIF1<0的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若當(dāng)SKIPIF1<0時(shí)，不等式SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例71．（2023·浙江·杭州高級(jí)中學(xué)高三期中）定義域?yàn)镾KIPIF1<0的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若SKIPIF1<0時(shí)，SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例72．（2023屆山西省榆林市高三二模理科數(shù)學(xué)試卷）定義域?yàn)镾KIPIF1<0的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【新題速遞】一、單選題1．（2023·廣西南寧·南寧二中?？家荒＃┮阎瘮?shù)SKIPIF1<0，若函數(shù)SKIPIF1<0，存在5個(gè)零點(diǎn)，則SKIPIF1<0（

）A．1 B．SKIPIF1<0 C．1或SKIPIF1<0 D．SKIPIF1<02．（2023春·陜西西安·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)為（

）A．1 B．3 C．4 D．53．（2023·江西景德鎮(zhèn)·統(tǒng)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．4 B．SKIPIF1<0 C．SKIPIF1<0 D．54．（2023春·內(nèi)蒙古赤峰·高三統(tǒng)考階段練習(xí)）已知實(shí)數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則下列說(shuō)法中，正確的是（

）．A．SKIPIF1<0 B．存在a，b，使得SKIPIF1<0C．SKIPIF1<0 D．存在a，b，使得直線SKIPIF1<0與圓SKIPIF1<0相切5．（2023·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0，SKIPIF1<0，動(dòng)點(diǎn)C在曲線T：SKIPIF1<0上，若△ABC面積的最小值為1，則SKIPIF1<0不可能為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023·浙江溫州·統(tǒng)考模擬預(yù)測(cè)）已知P為直線SKIPIF1<0上一動(dòng)點(diǎn)，過(guò)點(diǎn)P作拋物線SKIPIF1<0的兩條切線，切點(diǎn)記為A，B，則原點(diǎn)到直線SKIPIF1<0距離的最大值為（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．27．（2023春·江西贛州·高三贛州市贛縣第三中學(xué)校考期中）已知SKIPIF1<0，SKIPIF1<0，直線SKIPIF1<0與曲線SKIPIF1<0相切，則SKIPIF1<0的最小值是（

）A．16 B．12 C．8 D．48．（2023春·江蘇蘇州·高三蘇州中學(xué)?？茧A段練習(xí)）若關(guān)于x的不等式SKIPIF1<0對(duì)于任意SKIPIF1<0恒成立，則整數(shù)k的最大值為（

）A．-2 B．-1 C．0 D．1二、多選題9．（2023·江蘇蘇州·蘇州中學(xué)?？寄M預(yù)測(cè)）已知函數(shù)SKIPIF1<0，SKIPIF1<0，則下列說(shuō)法正確的是（

）A．SKI