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双空题 | 较难(0.4) | 2021·湖南长沙市·雅礼中学高一期末
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1 . 已知函数eqIdac415fef413e47578bd09ae9a0082607的定义域为eqId0005bc5d2f554698afeb8f199bc0cd81,值域为eqId7c50e527be944d1ab5c8dd64b33bce9d,用含eqId69f56ef2c88b4b73a560da59f5247a82的表达式表示eqIdd3e739f7f69d4432a1cf3eb7fe0548e9的最大值记为eqId6fcb96dc52ad4bbe9249e4d4a63bd35a,最小值记为eqIde60f9858d5b44fe693bf6a5749d3896b,设eqId1263480716f04b6f87eaa67d5012f2a2.
(1)若eqId6de346c6c5544c3789a2f4c94b576eb9,则eqId51fde35d76b44b3d930e178523e55730___________
(2)当eqId30744deedc344e60a3e708cc5a0e5ac7时,eqId0b1bec8f83bf4b6d890d276847e7a367的取值范围为___________.
解答题 | 困难(0.15) | 2021·北京东城区·高三一模
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2 . 设eqId84a7c056408047229d9dff9e99e04a35为正整数,若eqIdc3ea1b52d07349b79b96f41f18ee1a1e满足:①eqId702170ad176a49d5a02ab75215711204;②对于eqId8cc768ecfc6a41eba29d5550ca870428,均有eqIdb9653baaef2c4eec928fb7f07aaeb503;则称eqIdc13953f2514e4c8f9c8aaaf5241c33ac具有性质eqId9c9b858460a641e39d58587fca811f6c.对于eqIdc3ea1b52d07349b79b96f41f18ee1a1eeqId64dc3e5fab5f46f2982e731892eae188,定义集合eqIdabf75f71bb444a719f9e1ced6e9bcbef.
(1)设eqId4d8d459770af40c49b9509770dcb4cba,若eqId111d070ebfec479c910a3c51643696eb具有性质eqId9a0d1754ba964e02bbbca062330a66bb,写出一个及相应的eqIdd280db771c7944168ac2d159161ab755
(2)设eqIdc13953f2514e4c8f9c8aaaf5241c33aceqId4eb56f42ca674f2f9c9101b548763159具有性质eqId2e119dad43fe4bfbbacf18e73e713cfb,那么eqIdd280db771c7944168ac2d159161ab755是否可能为eqId4fbefc7ebe8948b09ece681fb1a1d2bf,若可能,写出一组eqIdc13953f2514e4c8f9c8aaaf5241c33aceqId4eb56f42ca674f2f9c9101b548763159,若不可能,说明理由;
(3)设eqIdc13953f2514e4c8f9c8aaaf5241c33aceqId4eb56f42ca674f2f9c9101b548763159具有性质eqId9c9b858460a641e39d58587fca811f6c,对于给定的eqIdc13953f2514e4c8f9c8aaaf5241c33ac,求证:满足eqId76ea333e3ddb499e8f9fae7ef3dd4f27eqId4eb56f42ca674f2f9c9101b548763159有偶数个.
3 . 已知函数eqId95e0f42fe9574038882c5c371144a210eqIdabfedbf6f82049589c7fbe6d5286a800.
(1)若关于eqIda9cd3f94eb8045438f75e9daccfa7200的方程eqIdd42e0952c00640eeb63e8f0f5ab3e9a4有两个不等根eqIdc13953f2514e4c8f9c8aaaf5241c33aceqId4eb56f42ca674f2f9c9101b548763159(eqId785ecd0bf11d408a9b7105b7bbd518a6),求eqId2453b3315cdc4c86b0cfa9d1eea41342的值;
(2)是否存在实数eqId70a27b6ddf6b478285353abb3b1f3741,使得对任意eqId3834c2a55623481793427bcb53f7e4d5,关于eqIda9cd3f94eb8045438f75e9daccfa7200的方程eqIdac530f656f1b4aac8f0584b7db1b5899在区间eqId9542badc38f84a1299c95a2201e91365上总有3个不等根eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73eqId2b48ba4c6112492987d51b451a7088c8,若存在,求出实数eqId70a27b6ddf6b478285353abb3b1f3741eqId0ebb808686bf47a5a7b8d751b83a7635的取值范围;若不存在,说明理由.
4 . 已知函数eqId9b086f7734f04fb59a46fc967f468dad若方程eqId16e0b0198514468dbff73f7182b28793有5个不等实根,则实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围是(   )
A.eqIdca7a51957af24eaaaf8a032e92774791B.eqIdd425ef50abbe45cabefd91b681a6225dC.eqId465420b50e824e20940b5554067bb974D.eqId4508942f3e0341c08018373699d7c976
填空题 | 较难(0.4) | 2021·全国高三专题练习(文)
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5 . 已知函数eqId8688692d786949f9a747c3d03a876c73(eqId8ccf61601cf049d8a2100ee27d5b2419eqId6158e6e525bf4cd7af7fb3a9a5562e56)的部分图象如图所示,eqId6f13759e937144069819aed2ae5a1057的图象与eqId072d7d6b911b42bc89207e72515ebf5f轴的交点的坐标是eqId92e73e2b41904318ab5e3d5894a91e80,且关于点eqIdf1cefc368b0941ec9681294d36fc66ea对称,若eqId6f13759e937144069819aed2ae5a1057在区间eqIdd0c8076ec596410babca6f07f1268a7b上单调,则eqIdf15782a6b93b49aeb4285c6f304dbe29的最大值是___________.
说明: figure
更新:2021/04/04组卷:138
单选题 | 较难(0.4) | 2021·天津和平区·高三一模
6 . 已知eqIde9edd995034840cfb557ea415074294a,设函数eqIdf9d4a2ef22bd429397d1e3e48d041856,若关于eqIda9cd3f94eb8045438f75e9daccfa7200的方程eqIdba76367ebf7e49e5bbf0e373c28120b5恰有两个互异的实数解,则实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围是(   )
A.eqIdc4a0e79aae284072becf8433d1b4c224B.eqId5230e6b0e7664f188e6cb0533cd3cd39
C.eqId5082630ee7b440c999ead62458510744D.eqId6100a225d90c43879dca1f3b4c848361
填空题 | 一般(0.65) | 2021·天津南开区·高三一模
7 . 已知eqId982da3835b7946d999cc8604a2ece266eqId8164502d09d44990ac4f2f73ea67e37aeqIdac0e1d339e204322883866de4e89dff3,则eqIdd306bb4240c84c91ac079d7eddc8e15f的最大值是______
8 . 已知函数eqIdfd66e9b9ccbc48adb637b52e4ebaf412.
(1)当eqIdd78df7c3aa4747a4b868757aa0e4e3f5时,求函数eqId78e7a51c9c5b47d8b163e2423ad9f088的零点;
(2)当eqId982da3835b7946d999cc8604a2ece266时,函数eqId4837c94ef0ff4dcf9b1dda4df363275aeqId7866cdd713694d23943f903588364452上为减函数,求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(3)当eqId41f04097a07d4d03941921a18fc42004时,是否存在实数eqId70a27b6ddf6b478285353abb3b1f3741,使得eqId4837c94ef0ff4dcf9b1dda4df363275a在闭区间eqId3e7a568e74e24e898022760c47c51566上的最大值为eqIdc052ddfbd4524f67a79e0e77c2e5656a?若存在,求出eqId70a27b6ddf6b478285353abb3b1f3741的值;若不存在,请说明理由.
10 . 已知eqId2c07a82215514a4eaf0b1325853b8f48eqId8164502d09d44990ac4f2f73ea67e37a,若eqId7108d42973bf4046abfc8edbc765d5e7有两零点eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73,且eqId06ac1d24d444488f843740fb259b2010,则eqIdc1d1d0a1c54e4ccc9308e8a97b4c4e0a的取值范围是___________.
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