组卷网>知识点选题>对称性,周期性与奇偶性综合问题
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2 . 已知函数eqId6a24f72e357c44e2bfe9930b537db7f4关于直线eqIdd5a6569623204652aada8c497a766e0a对称,对任意实数eqIdee96a7e70d7d4674b00f0471eb373095恒成立,且当eqIdc96f88fad8694a2d97ecd47143e4fdb5时,eqIde0d65503563a48c4a527d46d4c81b06f,则eqId08ae1785115b43b9b2c4490254424220(   )
A.eqId8898c1dc81824f3098bbeae74e8f11fdB.eqIdc052ddfbd4524f67a79e0e77c2e5656a
C.eqId29c898c2f6d5480e84ed6cd0dfc0930bD.eqIda86879ae304449a4a6e6461c485a1f13
3 . 已知定义在eqId3abaaedd36204e2cacb3fa4073cf99f5上的偶函数eqId10852d81bc184140a7780250c82c6929满足eqIdfbd4360a1fc04a6fbaf120a7b94b0a0d,当eqId27b1abecc2474a8f94b2a3b83e27e283时,eqIdcc694cc2a62e4f22a679d1fbe7f7fe17.给出下列四个结论:①eqId10852d81bc184140a7780250c82c6929的图象关于直线eqIdd5a6569623204652aada8c497a766e0a对称;②eqId10852d81bc184140a7780250c82c6929eqId5167ebf529b544b6939793f11fee2ac2上为减函数;③eqId10852d81bc184140a7780250c82c6929的值域为eqIdd5962c71196d40b28b2ca0d7b748b66d;④eqId27d50a351f2446a997ed8284268c656d有4个零点,其中正确结论的是(   )
A.①④B.②③C.①③④D.①②③
4 . 已知函数eqId10852d81bc184140a7780250c82c6929是定义在eqId38a1a72a865d4179b3b243977e23dce4上的奇函数,满足eqId02c07cc43df6451ab25498ac1dd81654,当eqId85eb53575dd34c888bbb489e15f1b57e时,eqId70c988825b38411483f8e2e98410b9e2,且eqId3c17b9d6586b49e285d7bcb2c06e54e7,则eqIde447d3dcefb442369fec3cbe4fc89458(   ).
A.eqId595df7631e1d467d91c88a838d918329B.0
C.eqIdb4af97a0ae204ab0907d054362bbaadfD.2021
5 . 设函数eqId6f13759e937144069819aed2ae5a1057的定义域为eqId7dcd2312d0bf4bb1befdfcc170e45791,且eqIdb0dadb5725d84bc99d53cc3aa6ab9992是偶函数,eqId996893f38aac40ab9a1d1fcb387c02da是奇函数,则下列说法一定正确的有(   )
eqId5b4cc6a1bd2d47b191d5e0362219e98a;   ②eqIdd108cccf75894b4ea93a181e9ddbf210;③eqIdc4cad54c36a64973a90a54eb0452df33;   ④eqIde6b228af1a3646bfbc6218ec78875d8a
A.4个B.3个C.2个D.1个
6 . 函数eqId9b37d03e47a347fc8fab9f814ba5fac4eqId7dcd2312d0bf4bb1befdfcc170e45791上的奇函数,满足eqId9b8db5436b974415aa75260f5963d208,当eqId980697563fdd40c3ba69df4b212b6e85时,有eqIdb9f404bcbb5744e78b834cd34568aaa5,求eqId0ee0b3f6e4144bc9a40bab1487fd20e2的值(   )
A.0B.1C.eqIda6b19fa9a22040fbb2cb05b8a778b847D.eqId62a9c09bbf2d4de6b70018364f7b1716
7 . 已知eqIde4a0e3706b56447b90fe1b2781f91b14是周期为4的奇函数,且当eqId513975578fb64836aa2e74f2f6b823b3时,eqIdd6ba3e7cc0a7419a9778bc917d4896ab,设eqId792317e7478d45b9b4f6d771534197b0,则(   )
A.函数eqId4188becfc28f4c4887a660b58a6169ec为周期函数
B.函数eqId4188becfc28f4c4887a660b58a6169ec的最大值为2
C.函数eqId4188becfc28f4c4887a660b58a6169ec在区间eqId58ceaae7a9b642daa67de2eb315c1d56上单调递增
D.函数eqId4188becfc28f4c4887a660b58a6169ec的图象既有对称轴又有对称中心
单选题 | 较难(0.4) | 2021·全国高三月考
8 . 已知函数eqId10852d81bc184140a7780250c82c6929是定义域为eqId7dcd2312d0bf4bb1befdfcc170e45791的偶函数,eqId7312d32126e742e493bbb406d4178b23,当eqId0b2539d8626345678ff21ec187987682时,eqId0a25c39bc5d24aee8d1e3ab45d627d83,则函数eqId8a1ccaf8eac9411eb2a9c232fdb76713与函数eqId9b37d03e47a347fc8fab9f814ba5fac4交点的个数为(   )
A.6B.7C.12D.14
9 . 已知函数eqId6f13759e937144069819aed2ae5a1057在实数集eqId7dcd2312d0bf4bb1befdfcc170e45791上具有下列性质:①直线eqIdd5a6569623204652aada8c497a766e0a是函数eqId6f13759e937144069819aed2ae5a1057图象的一条对称轴;②eqIda870e259737f407e9cf21e918ffc4b15;③当eqIdc6fb115f9d104e2a85a0ff8ec2f61bc8时,eqId7900b2cd7480482b99007e9c879fc681,则(   )
A.eqIda30b439f8baf4742beb6bd7144297e0bB.eqIde01e6a3b51294c4787847c1312c20644
C.eqIdcaf6480e8134429bb8323159c36ea7bbD.eqId66343f310cc046e2a67defe8ef31d94d