新高考數(shù)學(xué)一輪復(fù)習(xí) 函數(shù)專項(xiàng)重難點(diǎn)突破專題19 函數(shù)中的新定義問(wèn)題(原卷版)

專題19函數(shù)中的新定義問(wèn)題一、單選題1．若一系列函數(shù)的解析式和值域相同，但定義域不相同，則稱這些函數(shù)為“同值函數(shù)”，例如函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0即為“同值函數(shù)”，給出下面四個(gè)函數(shù)，其中能夠被用來(lái)構(gòu)造“同值函數(shù)”的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．高斯是德國(guó)著名的數(shù)學(xué)家，近代數(shù)學(xué)奠基者之一，享有“數(shù)學(xué)王子”的美譽(yù)，用其名字命名的“高斯函數(shù)":設(shè)SKIPIF1<0，用SKIPIF1<0表示不超過(guò)SKIPIF1<0的最大整數(shù)，則SKIPIF1<0稱為高斯函數(shù)，也稱取整函數(shù)，例如:SKIPIF1<0，已知SKIPIF1<0，則函數(shù)SKIPIF1<0的值域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．高斯是德國(guó)著名的數(shù)學(xué)家，近代數(shù)學(xué)奠基者之一，享有“數(shù)學(xué)王子”的稱號(hào)，設(shè)SKIPIF1<0，用SKIPIF1<0表示不超過(guò)SKIPIF1<0的最大整數(shù)，SKIPIF1<0也被稱為“高斯函數(shù)”，例如SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，設(shè)SKIPIF1<0為函數(shù)SKIPIF1<0的零點(diǎn)，則SKIPIF1<0（

）.A．2 B．3 C．4 D．54．若直角坐標(biāo)系內(nèi)兩點(diǎn)M、N滿足條件①M(fèi)、N都在函數(shù)y的圖象上②M、N關(guān)于原點(diǎn)對(duì)稱，則稱點(diǎn)對(duì)SKIPIF1<0是函數(shù)y的一個(gè)“共生點(diǎn)對(duì)”（點(diǎn)對(duì)SKIPIF1<0與SKIPIF1<0看作同一個(gè)”共生點(diǎn)對(duì)”），已知函數(shù)SKIPIF1<0，則函數(shù)y的“共生點(diǎn)對(duì)”有（

）個(gè)A．0 B．1 C．2 D．35．已知SKIPIF1<0，符號(hào)SKIPIF1<0表示不超過(guò)x的最大整數(shù)，若函數(shù)SKIPIF1<0有且僅有2個(gè)零點(diǎn)，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SKIPIF1<0，用SKIPIF1<0表示SKIPIF1<0，SKIPIF1<0中的最大者，記為：SKIPIF1<0．當(dāng)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0的最小值為（

）A．0 B．1 C．2 D．47．若函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，若存在實(shí)數(shù)SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，則稱SKIPIF1<0是“局部奇函數(shù)”．若函數(shù)SKIPIF1<0為SKIPIF1<0上的“局部奇函數(shù)”，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．對(duì)于定義在區(qū)間SKIPIF1<0上的函數(shù)SKIPIF1<0，若滿足：SKIPIF1<0且SKIPIF1<0，都有SKIPIF1<0，則稱函數(shù)SKIPIF1<0為區(qū)間SKIPIF1<0上的“非減函數(shù)”，若SKIPIF1<0為區(qū)間SKIPIF1<0上的“非減函數(shù)”，且SKIPIF1<0，又當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0恒成立，下列命題中正確的有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．設(shè)函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，如果對(duì)任意的SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，總有SKIPIF1<0成立，則稱函數(shù)SKIPIF1<0在SKIPIF1<0上為線增函數(shù)．下列函數(shù)中在其定義域上為線增函數(shù)的有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<010．設(shè)函數(shù)SKIPIF1<0的定義域?yàn)锳，若對(duì)于A內(nèi)任意兩個(gè)值SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0，則稱SKIPIF1<0具有T性質(zhì).下列函數(shù)中具有T性質(zhì)的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．設(shè)函數(shù)SKIPIF1<0，SKIPIF1<0定義域交集為SKIPIF1<0，若存在SKIPIF1<0，使得對(duì)任意SKIPIF1<0都有SKIPIF1<0，則稱SKIPIF1<0構(gòu)成“相關(guān)函數(shù)對(duì)”.則下列所給兩個(gè)函數(shù)構(gòu)成“相關(guān)函數(shù)對(duì)”的有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<012．已知符號(hào)函數(shù)SKIPIF1<0，偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則下列結(jié)論不正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空題13．對(duì)于函數(shù)SKIPIF1<0，若在其圖象上存在兩點(diǎn)關(guān)于原點(diǎn)對(duì)稱，則稱SKIPIF1<0為“倒戈函數(shù)”，設(shè)函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的“倒戈函數(shù)”，則實(shí)數(shù)m的取值范圍是_______.14．已知函數(shù)SKIPIF1<0，SKIPIF1<0，對(duì)任意的a，b，SKIPIF1<0，都存在以SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為三邊的三角形，則稱該函數(shù)為三角形函數(shù).若函數(shù)SKIPIF1<0是三角形函數(shù)，則實(shí)數(shù)m的取值范圍是______.15．對(duì)于函數(shù)SKIPIF1<0，如果存在區(qū)間SKIPIF1<0，同時(shí)滿足下列條件：①SKIPIF1<0在SKIPIF1<0上是單調(diào)的；②當(dāng)SKIPIF1<0的定義域是SKIPIF1<0時(shí)，SKIPIF1<0的值域是SKIPIF1<0，則稱SKIPIF1<0是該函數(shù)的“倍值區(qū)間”．若函數(shù)SKIPIF1<0存在“倍值區(qū)間”，則a的取值范圍是______．16．對(duì)于三次函數(shù)SKIPIF1<0，給出定義：設(shè)SKIPIF1<0是SKIPIF1<0的導(dǎo)數(shù)，SKIPIF1<0是SKIPIF1<0的導(dǎo)數(shù)，若方程SKIPIF1<0有實(shí)數(shù)解SKIPIF1<0，則稱點(diǎn)SKIPIF1<0為曲線SKIPIF1<0的“拐點(diǎn)”，可以發(fā)現(xiàn)，任何一個(gè)三次函數(shù)都有“拐點(diǎn)”.設(shè)函數(shù)SKIPIF1<0，則SKIPIF1<0SKIPIF1<0______.四、解答題17．對(duì)于實(shí)數(shù)a和b，定義運(yùn)算“*”：SKIPIF1<0，設(shè)SKIPIF1<0.(1)求SKIPIF1<0的解析式；(2)關(guān)于x的方程SKIPIF1<0恰有三個(gè)互不相等的實(shí)數(shù)根，求m的取值范圍.18．設(shè)函數(shù)的定義域?yàn)镾KIPIF1<0，如果存在SKIPIF1<0，使得SKIPIF1<0在SKIPIF1<0上的值域也為SKIPIF1<0，則稱SKIPIF1<0為“A佳”函數(shù).已知冪函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)是單調(diào)增函數(shù).(1)求函數(shù)SKIPIF1<0的解析式.(2)函數(shù)SKIPIF1<0是否為“A佳”函數(shù).若是，請(qǐng)指出所在區(qū)間；若不是，請(qǐng)說(shuō)明理由.19．已知函數(shù)SKIPIF1<0，若點(diǎn)SKIPIF1<0在函數(shù)SKIPIF1<0圖像上運(yùn)動(dòng)時(shí)，對(duì)應(yīng)的點(diǎn)SKIPIF1<0在函數(shù)SKIPIF1<0圖像上運(yùn)動(dòng)，則稱函數(shù)SKIPIF1<0是函數(shù)SKIPIF1<0的相關(guān)函數(shù).(1)求函數(shù)SKIPIF1<0的解析式；(2)對(duì)任意的SKIPIF1<0的圖像總在其相關(guān)函數(shù)圖像的上方，求實(shí)數(shù)SKIPIF1<0的取值范圍.20．若在定義域內(nèi)存在實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0成立，則稱函數(shù)有“飄移點(diǎn)”SKIPIF1<0．(1)函數(shù)SKIPIF1<0是否有“飄移點(diǎn)”？請(qǐng)說(shuō)明理由；(2)證明函數(shù)SKIPIF1<0在SKIPIF1<0上有“飄移點(diǎn)”；(3)若函數(shù)SKIPIF1<0在SKIPIF1<0上有“飄移點(diǎn)”，求實(shí)數(shù)a的取值范圍．21．設(shè)的數(shù)的定義域?yàn)镾KIPIF1<0，若存在正實(shí)數(shù)SKIPIF1<0，使得對(duì)于任意SKIP