解题方法
1 . 已知函数
.
(1)用单调性定义证明:
在
上单调递增;
(2)若函数
有3个零点
,满足
,且
.
①求证:
;
②求
的值(
表示不超过
的最大整数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247d7790d83be16bc74aa5e5d12dd63.png)
(1)用单调性定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f8994d83bf4a688c0ab897a5a40fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1cc5cfec94bc5686b41b043acdc8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d995c5d2e1e0305d805032e18997986a.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28cbe8f17c4472d8663f9ccbe3b98f6.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59077d1948911b13d68a572eadbca3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d82a8a3968ec0509bf3c338a939fb07.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/fa614b5d-38d8-419e-b9bc-3c58f1ef717a.png?resizew=173)
(1)完成下列表格,并在坐标系中描点画出函数
的简图;
(2)根据(1)的结果,若
(
),试猜想
的值,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d82a8a3968ec0509bf3c338a939fb07.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/fa614b5d-38d8-419e-b9bc-3c58f1ef717a.png?resizew=173)
(1)完成下列表格,并在坐标系中描点画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d82a8a3968ec0509bf3c338a939fb07.png)
(2)根据(1)的结果,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
1 | 2 | 4 | |||
您最近一年使用:0次
解题方法
3 . 函数的性质通常指函数的定义域、值域、单调性、奇偶性、零点等.已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b768fd17982b07fc369d72e1049807.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/5d557983-b0d7-4fc0-a63d-8f37b8e47c68.png?resizew=216)
(1)研究并证明函数
的性质;
(2)根据函数
的性质,画出函数
的大致图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b768fd17982b07fc369d72e1049807.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/5d557983-b0d7-4fc0-a63d-8f37b8e47c68.png?resizew=216)
(1)研究并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)根据函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
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4 . 定义:给定函数
,若存在实数
、
,当
、
、
有意义时,
总成立,则称函数
具有“
性质”.
(1)判别函数
是否具有“
性质”,若是,写出
、
的值,若不是,说明理由;
(2)求证:函数
(
且
)不具有“
性质”;
(3)设定义域为
的奇函数
具有“
性质”,且当
时,
,若对
,函数
有5个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63d7758a927384c13052ae432c20a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe17821ea81c6fec60bd5273901bd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ecb084837b614de935871d8f3dd2e1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c16d349946f1a9fbc12b28e7e9321c.png)
(1)判别函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d6e08526a91f8dfd160e7da2f92a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c16d349946f1a9fbc12b28e7e9321c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c16d349946f1a9fbc12b28e7e9321c.png)
(3)设定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae15be500f98d647a07fee39c95d041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ca276a67d4eca39a3c57dfab895e48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835eec12ec99561a3655c296570d75be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0db56c33be80c68078d92ba0ca47bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
5 . 定义:若将函数
的图象平移可以得到函数
的图象,则称函数
,
互为“平行函数”.已知
,
互为“平行函数”.
(1)判断并证明函数
的单调性;
(2)求实数a的值;
(3)求由函数
的图象、函数
的图象及y轴围成的封闭图形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c34d64a7bea0629324b9105d94556ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b8100c54a46bb7f8ba778307d7b03d.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求实数a的值;
(3)求由函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a5ff72ba4e9d01ecf0c0fe07a48058.png)
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名校
解题方法
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a296c144fc9626f81ae59d6dc1d6a80.png)
的图像;
(2)求
;
(3)求方程
的解集,并说明当整数
在何范围时,
.有且仅有一解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a296c144fc9626f81ae59d6dc1d6a80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981db5e1425f4510580273488f6e1fd0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549f9c4a708ba21ecadd712e2df626a4.png)
(3)求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b7bff9b2431134f7683a9cc4e68acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb291880ef86317d079c0e0b349403e5.png)
您最近一年使用:0次
2023-12-09更新
|
179次组卷
|
6卷引用:黑龙江省齐齐哈尔市克东县第一中学2023-2024学年高一上学期12月月考数学试卷
解题方法
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7f673cf793364aad2543ee8ae06228.png)
(1)请在网格纸中画出
的简图,并写出函数的单调区间(无需证明);
(2)定义函数
在定义域内的
,若满足
,则称
为函数
的一阶不动点,简称不动点;若满足
,则称
为函数
的二阶不动点,简称稳定点.
①求函数
的不动点;
②求函数
的稳定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7f673cf793364aad2543ee8ae06228.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/3dd251f6-1acf-44cf-b925-66705e04e25c.png?resizew=210)
(1)请在网格纸中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)定义函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de4841073ba41dc0e7b976759c3cd4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52dc0a7f95a39091a2f11d80cc8579f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a576aa37d6f504669b40b7b38cb92694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
②求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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名校
解题方法
8 . 已知函数
的图象可由函数
(
且
)的图象先向下平移2个单位长度,再向左平移1个单位长度得到,且
.
(1)求
的值;
(2)若函数
,证明:
;
(3)若函数
与
在区间
上都是单调的,且单调性相同,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e6f7234a6a37987de4cdce6f026331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93acdd1905e7b9374f0644820fb3fd71.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f4b6dabbadf37d201eadf7486dc98c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abea70e7e8122478683bc072aa38095.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b9a99afeadaec62a56019ff61e04c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496fd07ac35a34a6d0edfead2aeef41a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-11-23更新
|
343次组卷
|
2卷引用:河南省部分学校2023-2024学年高一上学期期中大联考数学试题
9 . 规定:若函数
的图象与函数
的图象有三个不同的公共点,则称这两个函数互为“兄弟函数”,其公共点称为“兄弟点”..
(1)下列三个函数:①
;②
;③
,其中与二次函数
互为“兄弟函数”的是______(只需填写序号,无需说明理由);
(2)若函数
与
互为“兄弟函数”,
是其中一个“兄弟点”的横坐标.
①求实数
的值;②求另外两个“兄弟点”的横坐标;
(3)若函数
(
)与
互为“兄弟函数”,三个“兄弟点”的横坐标分别为
,且
,若存在
使得不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
(1)下列三个函数:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8684443809254c64330bb349b473bda5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57fec8a77d00c7ceb55311eb1f149055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5186c7e510ec3f901f2094617be51b80.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61282ea8fc4d98ab57485658ba354bfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4047fefd895cdb94e6ccb72ba40081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63973dba6a9752c3d4b5b1cb6341d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b331c1454be742ab3a3885755c775005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671e7803ebb9e90f896bcdd0d0b43e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
10 . 已知二次函数的解析式为
.
(1)求解方程
,并写出方程的解集;
(2)比较下列
和
的大小;
(3)在平面直角坐标系下,作出二次函数
的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/620fff76456e4080c41c51661171c66f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/72a5819c-e54c-48c0-8b1e-fab9419ad5ca.png?resizew=174)
(1)求解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b0b55c3297ce66c96d1559d76971f4.png)
(2)比较下列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fcf521b88a7dbaf324df26cf67fcda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e592d76fd3ef30e964393a1eff2624.png)
(3)在平面直角坐标系下,作出二次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/620fff76456e4080c41c51661171c66f.png)
您最近一年使用:0次