组卷网>知识点选题>利用奇偶性、周期性和单调性求解函数问题
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1 . 已知函数eqId236afbc3d13843308fe9f6b98c43f74ceqIdb11128ab514a4e27bb0af2c2168f27d2,且eqId10852d81bc184140a7780250c82c6929是偶函数.
(1)求eqId70a27b6ddf6b478285353abb3b1f3741的值;
(2)若关于eqIda9cd3f94eb8045438f75e9daccfa7200的方程eqId5a84de46f7fe483cbd703a071dd2d5f1有实数解,求实数eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围.
2 . 已知eqId6f13759e937144069819aed2ae5a1057是定义在eqId7dcd2312d0bf4bb1befdfcc170e45791上的奇函数,且eqId6f13759e937144069819aed2ae5a1057eqIdd8eb8a663c154199a3f16c722a707785上的图像如图所示,那么eqIdac121730997d49c1b6e9356c505f15d1的解集为(   )
说明: figure
A.eqIda624fd6d209944dcb11a687a9aef00f1B.eqIdb42d00e8d02b40988d6bd3c49bfc23a0
C.eqId208cfe831ea0470d93fcd44b8c4ac631D.eqId6e3820f5c0db4a5592b86647949e5716
6 . (1)已知数列eqId50623a2ce8b5456c9d012c2d2d27c438,其中eqIde7fa766ad970441190913eb77bb92ee1,且数列eqIdb3e3b364e9f84387b06e79193f2a39cc为等比数列,求常数P
(2)设函数eqId4d3e93a6d87549de932f2ff7ade9eadb定义域为R,当eqId4db620a5946b4ee0a9f530f35a6d505a时,eqId4157df7d4b044f62862a09a132e9f439,且对于任意的xeqIda96c35333bce498fac43d585fdcaf8c2,有eqIdd3f90a1b9d6f4ce4bf28b92bf498b748成立,数列eqId054d5a7de5684002909fe944c86227c2满足eqId84af6848c7dd45b78800f79aa0dba4c5,且eqId00f664fc2db342bca09b48d9e612fbffeqId6c2146ec6df54fc9af9b2aef04489c8b).求数列eqId054d5a7de5684002909fe944c86227c2的通项公式并证明.
7 . 已知eqId10852d81bc184140a7780250c82c6929eqId7dcd2312d0bf4bb1befdfcc170e45791上的以eqId8898c1dc81824f3098bbeae74e8f11fd为周期的奇函数,则eqIdd0bcb84fd7df46249f2947b77223ed3c___________eqIdaacfc4418a30410c89a991bc338c08c0___________.
8 . 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
9 . 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
10 . 已知函数eqId8ae3fe95bb0148c888dd746adfa55dc5有如下性质:如果常数eqId982da3835b7946d999cc8604a2ece266,那么该函数在区间eqIde56a1661b6bc4a329f73a36680f43367上是减函数,在eqIdb2a6358024b442a0b40f9251a61b84c0上是增函数.
(1)如果函数eqId11ad451ccfab47a18b19f09cb5828c58eqIdaa1312dcc8e24925b421f7767761a363)的值域为eqId73871bff25af429da224f881aedc214d,求b的值;
(2)研究函数eqId9a66ba83bd26427684726738a25b6177(常数eqIde15d6f79043c484f8a85c084e5e6d722)在定义域上的单调性,并说明理由;
(3)对函数eqId8ae3fe95bb0148c888dd746adfa55dc5eqId1879f31b7ed14fd5b173c1e24362c948(常数eqId982da3835b7946d999cc8604a2ece266)作出推广,使它们都是你所推广的函数的特例.研究推广后的函数的单调性(只须写出结论,不必证明),并求函数eqIdfbe6142878364c4bae489019b508283an是正整数)在区间eqIdf4d3aaf6f2cb4903b6724a4f6781c6dc上的最大值和最小值(可利用你的研究结论).