组卷网>知识点选题>分离常数法求函数值域
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1 . 设eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,定义非零向量eqId4126706d912b4533b4b7162b384abf44的“相伴函数”为eqId5cbcc06b2b6748c695d4aa404eddd8eceqId5a3fcf16951b4107948a763f4077fe28称为函数eqId5cbcc06b2b6748c695d4aa404eddd8ec的“相伴向量"
(1)设函数eqId3ccb0835b52f4344aecedc6e3c250737,求函数eqId28c4c21271884dfeac29ce0222782376的相伴向量eqId868498ff9fa642879b7d44341bb0282c
(2)记eqIda159be535b1c4c91bfd67824bedd3199的“相伴函数"为eqId10852d81bc184140a7780250c82c6929,若方程eqId0fa0d28bd5284c1e81db67f9b01d66cc在区间[0,2eqIdf1470514d3384b7d8224a7712ab506bd]上有且仅有四个不同的实数解,求实数eqId4d2187284c5d4de29906363f7d21f60f的取值范围;
(3)已知点eqId38a73ac878314b8490313a1a5d5c6219满足eqId2673d9feb8c5425ba3444c8dea185e19,向量eqId868498ff9fa642879b7d44341bb0282c的“相伴函数”eqId10852d81bc184140a7780250c82c6929eqId02b4fd87b6dc469297673255c63eed1c处取得最大值,当点eqId2e472e2834814474a91b8ffcdc28fbcf运动时,求eqId5d0340ec8e6a4ae88e067690b9e1b04b的取值范围.
2 . 如图,棱长为1的正方体eqId588284d93dc5489295f8f224f8e30d13中,点eqIdbedf755e0fdb4d078d6859360706b163为线段eqId710b690db05c4a9ca514d234b961f314上的动点,点eqId71891062a8724584af9a2c4c77cd566e分别为线段eqId5d322b2942014a9f9bae1e86588819b0的中点,则下列说法错误的是(   )
说明: figure
A.eqId7f1858a7ddc34459bc630164d2bfab7eB.三棱锥eqIdad308a2cf1154b08aadbc5685592c312的体积为定值
C.eqId07ff6988f79f458fa2171321bf2bd45eD.eqId6a904be88ebb4e00862d26d4d25b3fbd的最小值为eqId5f51ce9cc7fe4412baeb871cceb26665
填空题 | 较易(0.85) | 2021·全国
3 . 当eqId93cb4ffc65d44e02b1bb018aef400c5c时,函数eqId36c092b42a7044cb9fe4f8019a0cbe31的最小值为________
更新:2021/09/18组卷:252
单选题 | 较易(0.85) | 2021·天津南开中学高三月考
4 . 已知定义在区间eqId6678935cac174d368ab1d1dc5fa27d03上的函数eqIdb5fde55f5bf14b89a2373e5bf4f697ef,其值域为(   )
A.eqId1a96077961f74b86991ba01fd64c7d75B.eqId5b6378fa3c894d40a580659643023ca6
C.eqIda68739b686f248519b849bde52a20490D.eqId5f14e430fe4a4d8d97ab199059741aff
5 . 如图,设eqId64b9b599fdb6481e9f8d9a94c102300b中角eqId10bbe48f886a4fa78fdf8c1fd064f9b4所对的边分别为eqIdbd4ee6a03cce4065a71cef97ef1d3562eqId0627be51821d4be7b3e024a354815d64边上的中线,已知eqIdda43591caa9542f780355a1d58dae3c1eqIdcddca1c7f0f548c5803eb235a32c2436.
说明: figure
(1)求b边的长度;
(2)求eqId64b9b599fdb6481e9f8d9a94c102300b的面积;
(3)设点eqId7758afa01251432a962db25cff5ae306分别为边eqIddea509e7b8a84270b44d4c7cc675dc0e上的动点,线段eqId1a0830891ff846de8422ea80714ecab4eqId8a76bbe21fb549e3a9c2038d58c7a3d8G,且eqIdfd61c954d0ae459f9de80cf8b9529a8d的面积为eqId64b9b599fdb6481e9f8d9a94c102300b面积的一半,求eqIda6bb27461f324619beb940227d699c3f的最小值.
6 . 已知点eqIdd083ab0d56df45c388700271956a70ebeqIdc27f89d973914990bcb46021992dae6d是函数eqIdc3c3de1e2d574b8c8192f95927fb800aeqId30c79e7c1f9d49289754bd19c693e50d图象上的任意两点,角eqId145940d03af4447eabd753d76abd2a1d的终边经过点eqId9e1bb286d5cc4b58bfead511b861d376,且当eqIdf0d7fcc8117a4a84ae0b78a8cb6fb7db时,eqId8750dd7121c840c1b3194aadb1a2a4fe的最小值为eqId43059a1babed4850ab90728e475e4ce1.若eqId632e692741014f59b4d1de8f945ccc0d,不等式eqIdffcee8dac7204353b7ce81e31d5da9b6恒成立,则实数eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围是_____________.
单选题 | 一般(0.65) | 2021·沧源佤族自治县民族中学
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7 . 已知函数eqId37e9ffdd23764789a4459ceb811567aa的最小值为2,则a的取值范围是(   )
A.eqId687b6c04f14249ac871f0d13ab5d7fc1B.eqId7162192b280e4a7bbb333f3c01c82d2fC.eqId8db0af08c8a74fe5913bfbf161d7f661D.eqIdbdbd83dd07134985bcddc63d90046465
8 . 函数eqId13a2242eaefc42cc903c6d5056fd0da1在区间eqIdf173839cbdf549429066610d1a327f06上的最小值为__________
10 . 已知函数eqId74c47c004331445f803d12d20f13e05c,则函数具有下列性质(   )
A.函数eqId10852d81bc184140a7780250c82c6929的图象关于点eqIdc65c54b9c3f847739bfb845e28d63d8c对称B.函数eqId10852d81bc184140a7780250c82c6929在定义域内是减函数
C.函数eqId10852d81bc184140a7780250c82c6929的图象关于直线eqId304afd9f2ec84e138ab539275a5edd19对称D.函数eqId10852d81bc184140a7780250c82c6929的值域为eqIdd1166c3b71c04335830a50f804e75ca2