新高考數(shù)學(xué)一輪復(fù)習(xí) 函數(shù)專(zhuān)項(xiàng)重難點(diǎn)突破專(zhuān)題05 分段函數(shù)(原卷版)

專(zhuān)題05分段函數(shù)真題再現(xiàn)1．（2023·北京·統(tǒng)考高考真題）設(shè)SKIPIF1<0，函數(shù)SKIPIF1<0，給出下列四個(gè)結(jié)論：①SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減；②當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0存在最大值；③設(shè)SKIPIF1<0，則SKIPIF1<0；④設(shè)SKIPIF1<0．若SKIPIF1<0存在最小值，則a的取值范圍是SKIPIF1<0．其中所有正確結(jié)論的序號(hào)是____________．2．（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_________．3．（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)__________．4．（2021·浙江·統(tǒng)考高考真題）已知SKIPIF1<0，函數(shù)SKIPIF1<0若SKIPIF1<0，則SKIPIF1<0___________.考點(diǎn)一分段函數(shù)函數(shù)值(解析式)一、單選題1．已知函數(shù)SKIPIF1<0，則SKIPIF1<0（

）A．5B．3 C．2 D．12．已知函數(shù)SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．-1 D．23．已知函數(shù)SKIPIF1<0，則SKIPIF1<0（

）A．4 B．8 C．16 D．324．已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（）.A．SKIPIF1<01 B．SKIPIF1<02 C．SKIPIF1<03 D．SKIPIF1<045．已知函數(shù)SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函數(shù)SKIPIF1<0，則SKIPIF1<0（

）A．4 B．5 C．6 D．77．已知函數(shù)SKIPIF1<0，則SKIPIF1<0（

）A．1 B．e C．SKIPIF1<0 D．SKIPIF1<08．若函數(shù)SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．函數(shù)f(x)的圖象如圖所示，則f(x)的解析式是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空題10．已知函數(shù)SKIPIF1<0，則SKIPIF1<0___________．11．已知函數(shù)SKIPIF1<0，則SKIPIF1<0___________．12．已知函數(shù)SKIPIF1<0，則SKIPIF1<0_________．13．設(shè)函數(shù)SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的解析式為_(kāi)___________．14．設(shè)SKIPIF1<0定義在SKIPIF1<0上且SKIPIF1<0，則SKIPIF1<0______．考點(diǎn)二分段函數(shù)定義域和值域一、單選題1．設(shè)函數(shù)SKIPIF1<0，SKIPIF1<0則SKIPIF1<0的值域是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．若定義運(yùn)算SKIPIF1<0，則函數(shù)SKIPIF1<0的值域是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題3．已知函數(shù)SKIPIF1<0，關(guān)于函數(shù)SKIPIF1<0的結(jié)論正確的是（

）A．SKIPIF1<0的定義域是R B．SKIPIF1<0的值域是SKIPIF1<0C．若SKIPIF1<0，則x的值為SKIPIF1<0 D．SKIPIF1<0三、填空題4．函數(shù)SKIPIF1<0的定義域是________.5．已知SKIPIF1<0，則SKIPIF1<0的值域是______；6．函數(shù)SKIPIF1<0的值域是______．7．已知函數(shù)SKIPIF1<0SKIPIF1<0的最大值為m，SKIPIF1<0的最小值為n，則SKIPIF1<0______．8．已知函數(shù)SKIPIF1<0，則SKIPIF1<0的最小值為_(kāi)________．四、雙空題9．函數(shù)y＝SKIPIF1<0的定義域?yàn)開(kāi)_______，值域?yàn)開(kāi)_______.10．如圖為一分段函數(shù)的圖象，則該函數(shù)的定義域?yàn)開(kāi)_______，值域?yàn)開(kāi)_______．五、解答題11．已知函數(shù)SKIPIF1<0的圖象如圖所示，其中SKIPIF1<0軸的左側(cè)為一條線段，右側(cè)為某拋物線的一段．(1)寫(xiě)出函數(shù)SKIPIF1<0的定義域和值域；(2)求SKIPIF1<0的值．考點(diǎn)三分段函數(shù)單調(diào)性一、單選題1．定義運(yùn)算：SKIPIF1<0，例如：SKIPIF1<0，SKIPIF1<0，則函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0和SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0和SKIPIF1<03．若函數(shù)SKIPIF1<0是SKIPIF1<0上的單調(diào)函數(shù)，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題4．已知函數(shù)SKIPIF1<0在R上單調(diào)遞增，則實(shí)數(shù)a的取值可以是（

）A．0 B．1 C．2 D．3三、填空題5．設(shè)函數(shù)SKIPIF1<0，SKIPIF1<0，則函數(shù)SKIPIF1<0的遞增區(qū)間為_(kāi)_______.6．函數(shù)SKIPIF1<0的單調(diào)增區(qū)間為_(kāi)_________.7．己知函數(shù)SKIPIF1<0滿足對(duì)任意SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0成立，則實(shí)數(shù)a的取值范圍是__________．8．已知函數(shù)SKIPIF1<0，設(shè)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的取值范圍是____________.四、雙空題9．函數(shù)SKIPIF1<0的單調(diào)性為_(kāi)_____；奇偶性為_(kāi)_____．五、解答題10．已知函數(shù)SKIPIF1<0(1)求SKIPIF1<0，SKIPIF1<0的值；(2)若SKIPIF1<0，求實(shí)數(shù)a的值；(3)直接寫(xiě)出SKIPIF1<0的單調(diào)區(qū)間．考點(diǎn)四分段函數(shù)求參一、單選題1．已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．1 D．22．設(shè)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．1 D．23．已知函數(shù)SKIPIF1<0SKIPIF1<0的值域?yàn)镾KIPIF1<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<04．已知函數(shù)SKIPIF1<0的最大值為0，則實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．若函數(shù)SKIPIF1<0，在R上單調(diào)遞增，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函數(shù)SKIPIF1<0，滿足對(duì)任意的實(shí)數(shù)SKIPIF1<0，SKIPIF1<0且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<07．已知函數(shù)SKIPIF1<0在SKIPIF1<0是減函數(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<08．函數(shù)SKIPIF1<0，若SKIPIF1<0互不相等，且SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題9．已知SKIPIF1<0，函數(shù)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0________．10．已知函數(shù)SKIPIF1<0．若SKIPIF1<0，則實(shí)數(shù)m的取值范圍是______．11．設(shè)函數(shù)SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)a＝_____．12．已知函數(shù)SKIPIF1<0且SKIPIF1<0，則正數(shù)SKIPIF1<0的值為_(kāi)_____.13．設(shè)函數(shù)SKIPIF1<0存在最小值，則SKIPIF1<0的取值范圍是________.14．已知SKIPIF1<0，若存在三個(gè)不同實(shí)數(shù)SKIPIF1<0使得SKIPIF1<0，則SKIPIF1<0的取值范圍是______．15．設(shè)SKIPIF1<0且SKIPIF1<0，已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0是遞增數(shù)列，則a的取值范圍是____．16．已知SKIPIF1<0，其中SKIPIF1<0且SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0___________．考點(diǎn)五解分段函數(shù)不等式一、單選題1．已知SKIPIF1<0,則使SKIPIF1<0成立的SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．已知函數(shù)SKIPIF1<0，則滿足不等式SKIPIF1<0的x的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．已知函數(shù)SKIPIF1<0，則不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．若SKIPIF1<0，且SKIPIF1<0的解集為SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0二、多選題7．已知SKIPIF1<0是定義在SKIPIF1<0的奇函數(shù)，且SKIPIF1<0時(shí)，SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0時(shí)，SKIPIF1