名校
1 . 对于一元三次函数
(
)图象上任一点
,若
在点
处的切线与
的图象交于另一点
,则称
为
的“伴随割点”,关于“伴随割点”,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19951f3364fb04433feed743bc37975d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.点![]() |
B.若点![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
2 . 已知函数
,给出下列四个结论:
①函数
是奇函数;
②
,且
,关于x的方程
恰有两个不相等的实数根;
③已知
是曲线
上任意一点,
,则
;
④设
为曲线
上一点,
为曲线
上一点.若
,则
.
其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d08e4a96cfcea8a303b56b35cafb47fb.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b10c7c83af99e5686133623e29c455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23899cffeb0d20e29e7212a7327c604a.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482ad28bbcbe8b8d384d84851a54386b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f614a56621170153a1a1c582a145ba.png)
④设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793894c733026e3f5900b31538fcb731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2dff006a89ed43e44492206e8516e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3d36c7faa45fe5dae65a800cb59c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778083c63e464acd369abc5e667c8d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f850a3ec66b1438ca4da2c30b6939ea9.png)
其中所有正确结论的序号是
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3 . 对于函数
,若实数
满足
,其中F、D为非零实数,则
称为函数
的“
笃志点”.
(1)若
,求函数
的“
笃志点”;
(2)已知函数
,且函数
有且只有3个“
笃志点”,求实数a的取值范围;
(3)定义在R上的函数
满足:存在唯一实数m,对任意的实数x,使得
恒成立或
恒成立.对于有序实数对
,讨论函数
“
笃志点”个数的奇偶性,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018a66c847609b6598fd455445021ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb270730495d3aa42e23c8b0d98ab3ae.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df18da1ecd1a83afc4544ee71f00c56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d5bd01306129e4b00b7af1888975fb.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889100ab0ad010cf68ae0f63244c7b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587f9f6a4bfc5bdc31b32b03353a0cc3.png)
(3)定义在R上的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6945674f1cb97c868dde84129106e55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674429107bdd48aa75e85a30d36e7276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc671b445f41402078b15e2ba6fdf8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb270730495d3aa42e23c8b0d98ab3ae.png)
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2023-10-26更新
|
626次组卷
|
2卷引用:上海市复旦大学附属中学2024届高三上学期10月月考数学试题
名校
解题方法
4 . 已知函数
,其中
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6f1cb607f6033a80262e00092b4d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52dda3ae004fe65451ceb01ee376da5f.png)
A.当![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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2023-10-03更新
|
700次组卷
|
2卷引用:辽宁省沈阳市实验中学2023-2024学年高三上学期9月月考数学试题
名校
解题方法
5 . 已知定义在
上的函数
的导函数为
,则下列错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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2023-06-15更新
|
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2卷引用:浙江省重点中学拔尖学生培养联盟2023届高三下学期6月适应性考试数学试题
名校
解题方法
6 . 已知函数
,函数
的最小值记为
,给出下面四个结论:
①
的最小值为0;
②
的最大值为3;
③若
在
上单调递减,则
的取值范围为
;
④若存在
,对于任意的
,
,则
的可能值共有4 个;
则全部正确命题的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efee94d8d161b6471d4c6e89a153af7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c82644f77c5455ceb7f94950e94273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/573490ed07601c52a92d4a374db57d95.png)
④若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ccecaf28ac8d62d16577082832dab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
则全部正确命题的序号为
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2023-03-07更新
|
1328次组卷
|
5卷引用:北京中央民族大学附属中学2023届高三零模数学试题
北京中央民族大学附属中学2023届高三零模数学试题(已下线)北京市中央民族大学附属中学2023届高三零模数学试题山东师范大学附属中学幸福柳分校2023-2024学年高一上学期期中考试数学试题(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)(已下线)专题6 绝对值函数中参数问题(每日一题)
名校
解题方法
7 . 已知函数
的定义域为D,若存在实数a,b,对任意的
,有
,且使得
均成立,则函数
的图像关于点
对称,反之亦然,我们把这样的函数
叫做“
函数.
(1)已知“
函数”的图像关于点
对称,且
时,
;求
时,函数
的解析式;
(2)已知函数
,问
是否为“
函数”?请说明理由;
(3)对于不同的“
函数”
与
,若
、
有且仅有一个对称中心,分别记为
和
,
①求证:当
时,
仍为“
函数”;
②问:当
时,
是否仍一定为“
函数”?若是,请说明理由;若不一定是,请举出具体的反例.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d877b154b2c2f42ebc9bb4c85faef9f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5ca6a673a07fe420e017b3e24d3887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
(1)已知“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d53e84446ab2d482dd8cdfeb27b402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df4cf16e39bff4aa2d482c90411d5ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129da6ef5f007a81bcfa5847fda1ed40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
(3)对于不同的“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d496307b8bab026701a3293ccde58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ea5dc4754e7173e6b6eed461c0e490.png)
①求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a4480988244a9d04ec293975db2cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfcc567b95a320abcb25509923cd001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
②问:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfcc567b95a320abcb25509923cd001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
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