高考數(shù)學二輪復(fù)習壓軸題專題02 函數(shù)概念與基本初等函數(shù)（新定義高數(shù)觀點選填壓軸題）（原卷版）

專題02函數(shù)概念與基本初等函數(shù)（新定義，高數(shù)觀點，選填壓軸題）目錄TOC\o"1-1"\h\u一、函數(shù)及其表示 1二、函數(shù)的基本性質(zhì) 2三、分段函數(shù) 4四、函數(shù)的圖象 5五、二次函數(shù) 7六、指對冪函數(shù) 7七、函數(shù)與方程 8八、新定義題 9一、函數(shù)及其表示1．（2023·江西·校聯(lián)考模擬預(yù)測）已知函數(shù)SKIPIF1<0，SKIPIF1<0，若對任意的SKIPIF1<0，存在SKIPIF1<0，使SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023春·甘肅白銀·高二校考期末）已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0則SKIPIF1<0的定義域為3．（2023春·內(nèi)蒙古巴彥淖爾·高二?？计谀┮阎瘮?shù)SKIPIF1<0定義域為SKIPIF1<0，則函數(shù)SKIPIF1<0的定義域為.4．（2023·全國·高一專題練習）已知函數(shù)SKIPIF1<0的值域為SKIPIF1<0，則常數(shù)SKIPIF1<0．5．（2023·全國·高三專題練習）求函數(shù)SKIPIF1<0的值域.6．（2023·全國·高三專題練習）當SKIPIF1<0時，求函數(shù)SKIPIF1<0的最小值.7．（2023·高一課時練習）若函數(shù)SKIPIF1<0滿足方程SKIPIF1<0且SKIPIF1<0，則：（1）SKIPIF1<0；（2）SKIPIF1<0．8．（2023·全國·高三專題練習）若SKIPIF1<0滿足關(guān)系式SKIPIF1<0，則SKIPIF1<0，若SKIPIF1<0，則實數(shù)m的取值范圍是．二、函數(shù)的基本性質(zhì)1．（2023春·遼寧鐵嶺·高二昌圖縣第一高級中學?？计谀┮阎瘮?shù)SKIPIF1<0，則不等式SKIPIF1<0的解集是（

）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023春·甘肅白銀·高二?？计谀┮阎x在SKIPIF1<0上的函數(shù)SKIPIF1<0在SKIPIF1<0單調(diào)遞增，且SKIPIF1<0是偶函數(shù)，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023秋·重慶九龍坡·高一重慶市楊家坪中學校考期末）若定義在SKIPIF1<0的奇函數(shù)SKIPIF1<0在SKIPIF1<0單調(diào)遞減，且SKIPIF1<0，則滿足SKIPIF1<0的SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2023·全國·高三專題練習）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023春·河北唐山·高二校聯(lián)考期末）已知函數(shù)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023春·廣西北?！じ叨y(tǒng)考期末）設(shè)函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，滿足SKIPIF1<0，且當SKIPIF1<0時，SKIPIF1<0.若對任意SKIPIF1<0，都有SKIPIF1<0成立，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·云南·云南師大附中?？寄M預(yù)測）已知函數(shù)SKIPIF1<0，SKIPIF1<0的定義域均為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是偶函數(shù)，且SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0關(guān)于直線SKIPIF1<0對稱 B．SKIPIF1<0關(guān)于點SKIPIF1<0中心對稱C．SKIPIF1<0 D．SKIPIF1<08．（2023春·新疆·高二統(tǒng)考期末）若奇函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，且SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0時，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2023·云南昭通·校聯(lián)考模擬預(yù)測）已知函數(shù)SKIPIF1<0是定義域為SKIPIF1<0上的奇函數(shù)，滿足SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．2 B．3 C．4 D．510．（2023春·安徽黃山·高二統(tǒng)考期末）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（多選）（2023秋·重慶渝中·高三重慶巴蜀中學校考階段練習）已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0是偶函數(shù)C．SKIPIF1<0的一個周期SKIPIF1<0 D．SKIPIF1<012．（多選）（2023春·河北保定·高二校聯(lián)考期末）定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0，則（

）A．SKIPIF1<0是奇函數(shù) B．SKIPIF1<0的最小正周期為4C．SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱 D．SKIPIF1<013．（2023春·遼寧沈陽·高二校考期末）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0關(guān)于SKIPIF1<0對稱，當SKIPIF1<0時，SKIPIF1<0.若SKIPIF1<0，則SKIPIF1<0.三、分段函數(shù)1．（2023·寧夏銀川·銀川一中?？寄M預(yù)測）設(shè)函數(shù)SKIPIF1<0，則SKIPIF1<0（

）A．4 B．5 C．6 D．72．（2023春·寧夏銀川·高二銀川一中?？计谀┮阎瘮?shù)SKIPIF1<0是SKIPIF1<0上的增函數(shù)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023春·吉林長春·高一校考開學考試）已知函數(shù)SKIPIF1<0滿足對任意實數(shù)SKIPIF1<0，都有SKIPIF1<0成立，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023春·吉林長春·高二長春外國語學校校考期末）已知定義在R上的奇函數(shù)滿足SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0（

）A．2 B．SKIPIF1<0 C．－2 D．－SKIPIF1<05．（2023春·江蘇蘇州·高一校聯(lián)考期末）已知函數(shù)SKIPIF1<0，則下列說法錯誤的是（

）A．SKIPIF1<0是單調(diào)遞增函數(shù) B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2023·河南·襄城高中校聯(lián)考三模）已知函數(shù)SKIPIF1<0的最大值為0，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023春·遼寧·高二校聯(lián)考階段練習）已知函數(shù)SKIPIF1<0若SKIPIF1<0，則SKIPIF1<0（

）A．4 B．3 C．2 D．18．（2023春·山西太原·高二太原五中校考階段練習）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0四、函數(shù)的圖象1．（2023春·云南保山·高二校聯(lián)考期末）函數(shù)SKIPIF1<0的圖象可能是（

）A． B．C． D．2．（2023春·廣東韶關(guān)·高二統(tǒng)考期末）SKIPIF1<0部分圖象大致是（

）A． B．

C．

D．3．（2023春·云南楚雄·高二統(tǒng)考期末）函數(shù)SKIPIF1<0的部分圖象大致為（

）A． B．C． D．4．（2023春·湖北武漢·高一華中師大一附中?？计谀┫铝兴膫€函數(shù)中的某個函數(shù)在區(qū)間SKIPIF1<0上的大致圖象如圖所示，則該函數(shù)是（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023春·河北滄州·高二統(tǒng)考期中）函數(shù)SKIPIF1<0的圖象大致為（

）A．

B．

C．

D．

6．（2023·內(nèi)蒙古赤峰·統(tǒng)考二模）函數(shù)SKIPIF1<0在SKIPIF1<0上的圖象大致為（

）A． B．C． D．五、二次函數(shù)1．（2023秋·陜西咸陽·高一統(tǒng)考期末）已知函數(shù)SKIPIF1<0與SKIPIF1<0的圖象上不存在關(guān)于SKIPIF1<0軸對稱的點，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023·全國·高三專題練習）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，則實數(shù)SKIPIF1<0的取值范圍是．3．（2023春·山西運城·高二康杰中學?？茧A段練習）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為1，則實數(shù)SKIPIF1<0的值為.4．（2023·江蘇·高一假期作業(yè)）如果函數(shù)SKIPIF1<0定義在區(qū)間SKIPIF1<0上，求SKIPIF1<0的值域．六、指對冪函數(shù)1．（多選）（2023春·廣西南寧·高二賓陽中學校聯(lián)考期末）已知SKIPIF1<0，則實數(shù)SKIPIF1<0，SKIPIF1<0滿足（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（多選）（2023春·福建福州·高二福州三中?？计谀┮阎瘮?shù)SKIPIF1<0，設(shè)SKIPIF1<0（SKIPIF1<0，2，3）為實數(shù)，SKIPIF1<0，且SKIPIF1<0，則（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱B．不等式SKIPIF1<0的解集為SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<03．（2023春·浙江紹興·高二統(tǒng)考期末）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足:SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，當SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023·河南·校聯(lián)考模擬預(yù)測）已知冪函數(shù)SKIPIF1<0的圖象過SKIPIF1<0，SKIPIF1<0，SKIPIF1<0（SKIPIF1<0）是函數(shù)圖象上的任意不同兩點，則下列結(jié)論中正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2023·吉林白山·統(tǒng)考二模）函數(shù)SKIPIF1<0的定義域為R，則實數(shù)a的取值范圍是（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023·貴州黔東南·凱里一中?？寄M預(yù)測）已知函數(shù)SKIPIF1<0，且SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0七、函數(shù)與方程1．（2023·貴州畢節(jié)·校考模擬預(yù)測）若函數(shù)SKIPIF1<0有唯一零點，則實數(shù)SKIPIF1<0（

）A．2 B．SKIPIF1<0 C．4 D．12．（2023春·福建福州·高二?？计谀┮阎瘮?shù)SKIPIF1<0，則方程SKIPIF1<0的解的個數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023春·江西南昌·高二南昌二中?？计谀┮阎瘮?shù)SKIPIF1<0，若SKIPIF1<0有四個不同的解SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0可能的取值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023春·江蘇鹽城·高一江蘇省響水中學?？计谀┮阎瘮?shù)SKIPIF1<0，若函數(shù)SKIPIF1<0有五個零點，則實數(shù)SKIPIF1<0的取值范圍是.5．（2023春·廣東廣州·高一?？计谥校┮阎瘮?shù)SKIPIF1<0，若關(guān)于x的方程SKIPIF1<0有四個不同的實數(shù)根，則實數(shù)a的取值范圍是．6．（2023春·遼寧大連·高二統(tǒng)考期末）已知函數(shù)SKIPIF1<0，若存在區(qū)間SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0的值域為SKIPIF1<0，且SKIPIF1<0，其中SKIPIF1<0表示不超過SKIPIF1<0的最大整數(shù)，則SKIPIF1<0的取值范圍為．7．（2023春·河北唐山·高二校聯(lián)考期末）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，滿足SKIPIF1<0，當SKIPIF1<0時，SKIPIF1<0，若方程SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)有實數(shù)解，則實數(shù)SKIPIF1<0的取值范圍為.八、新定義題1．（2023春·廣東·高一統(tǒng)考期末）嶺南古邑的番禺不僅擁有深厚的歷史文化底蘊，還聚焦生態(tài)的發(fā)展．下圖SKIPIF1<0是番禺區(qū)某風景優(yōu)美的公園地圖，其形狀如一顆愛心．圖SKIPIF1<0是由此抽象出來的一個“心形”圖形，這個圖形可看作由兩個函數(shù)的圖象構(gòu)成，則“心形”在SKIPIF1<0軸上方的圖象對應(yīng)的函數(shù)解析式可能為（

）

A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023·全國·高一專題練習）在數(shù)學中，布勞威爾不動點定理是拓撲學里一個非常重要的不動點定理，它可應(yīng)用到有限維空間，并構(gòu)成一般不動點定理的基石.布勞威爾不動點定理得名于荷蘭數(shù)學家魯伊茲?布勞威爾（L.E.J.Brouwer），簡單的講就是對于滿足一定條件的圖象不間斷的函數(shù)f(x)，存在一個點x0，使得f(x0)=x0，那么我們稱該函數(shù)為“不動點“函數(shù).下列為“不動點”函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023春·云南紅河·高一統(tǒng)考期末）2023年2月27日，學堂梁子遺址入圍2022年度全國十大考古新發(fā)現(xiàn)終評項目．該遺址先后發(fā)現(xiàn)石制品300多件，已知石制品化石樣本中碳14質(zhì)量N隨時間t（單位：年）的衰變規(guī)律滿足SKIPIF1<0（SKIPIF1<0表示碳14原有的質(zhì)量）．經(jīng)過測定，學堂梁子遺址中某件石制品化石樣本中的碳14質(zhì)量約是原來的SKIPIF1<0倍，據(jù)此推測該石制品生產(chǎn)的時間距今約（

）．（參考數(shù)據(jù)：SKIPIF1<0，SKIPIF1<0）A．8037年 B．8138年 C．8237年 D．8337年4．（2023春·江蘇南京·高一?？计谥校甏哪Ｐ蚐KIPIF1<0是由岡珀茨SKIPIF1<0提出，可作為動物種群數(shù)量變化的模型，并用于描述種群的消亡規(guī)律.已知某珍稀物種SKIPIF1<0年后的種群數(shù)量SKIPIF1<0近似滿足岡珀茨模型：SKIPIF1<0（當SKIPIF1<0時，表示2020年初的種群數(shù)量），請預(yù)測從哪一年年初開始，該物種的種群數(shù)量將不足2022年初種群數(shù)量的一半（

）SKIPIF1<0A．2031 B．2020 C．2029 D．2