1 . 我们知道,函数
的图象关于坐标原点成中心对称图形的充要条件是函数
为奇函数,这一结论可将其推广为:函数
的图象关于点
成中心对称图形的充要条件是函数
为奇函数.已知函数
.
(1)利用上述结论,证明:
的图象关于
成中心对称图形;
(2)判断并利用定义证明函数
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82aaa597a5aa6176863eda3fdf83e181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabb58d05e792a1ebebf1d4f1ff0e1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7149f31bc63c9852d6dd7638407a57f4.png)
(1)利用上述结论,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
(2)判断并利用定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
2 . 已知函数
是定义域为
的奇函数.
(1)求实数
的值;
(2)判断
的单调性(不需要证明);
(3)若存在
,使
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a63e4ea615b07bd813446d19063b30c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6160880daa2b7f329c96b549e3deafb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fc9da283c299b38d8eadc2acc7e5fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
3 . 已知函数
(
且
)在
上最大值和最小值的和为12.
(1)求实数a的值;
(2)令
,若
在区间
上有零点,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.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/9210e75c35fb455d0446eb7ddba7d79c.png)
(1)求实数a的值;
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ccf497a2b64231fc1438d9c011b7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c21caf0cf2582c2f7acbd43aee0511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
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2023-12-01更新
|
366次组卷
|
3卷引用:山东省泰安市肥城市第一高级中学2023-2024学年高一上学期12月月考数学试题
山东省泰安市肥城市第一高级中学2023-2024学年高一上学期12月月考数学试题广东省深圳外国语学校2023-2024学年高一上学期第二阶段考试数学试卷(已下线)【第三练】4.5.1函数的零点与方程的解 4.5.2用二分法求方程的近似解
名校
解题方法
4 . 已知函数
.
(1)若
,求
的单调区间
(2)若
有最大值3,求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8299220337d3e914bf635f5ada7056e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
5 . 已知函数
的定义域为
可以表示为一个偶函数
和一个奇函数
之和.
(1)求
和
的解析式;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df280046be1a000d06a7705a703c2e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0ef3d1ff1589da0cb326c4debc274f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa5490268aef89a31231367d695bae0.png)
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解题方法
6 . 已知函数
为定义在
上的奇函数.
(1)求a的值;
(2)试判断函数的单调性,并用定义加以证明;
(3)若关于x的方程
在
上有解,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b0ccc44b23df71e61c20192393e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求a的值;
(2)试判断函数的单调性,并用定义加以证明;
(3)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
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解题方法
7 . 已知函数
是定义在
上的奇函数.
(1)求
;
(2)证明:
在
上为增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ddf53e0adf06712a59e1d9f4631de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
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2023-02-21更新
|
177次组卷
|
2卷引用:山东省青岛市西海岸新区2022-2023学年高一下学期调研检测(分科考试)数学试题
8 . 设函数
(
且
).
(1)若
,试判断函数
的单调性,并加以证明;
(2)若已知
,且函数
在区间
上的最小值为
,求实数
的值.(提示:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f1a326456ba10c718efdcf7d525e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e273784487d908f05bfba0d705a67d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1b6a97182bf7e313389bd039241974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd286a5f69d138fe3d9b537eeecb82e8.png)
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解题方法
9 . 已知函数
是定义在R上的偶函数,其最小正周期为2,若
时,
,且满足
.
(1)当
时,求函数
的解析式;
(2)请判断函数
在
上的单调性(只判断不证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e46371f310e03a153a1698aad9d4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7652f36dcc03ec971cf266190e8107bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3471484b64504fc545398f52be830010.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20d1be3f52520e09f4a76b53b3d4481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)请判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f88173ef0c29bedd0155b7893d2474.png)
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解题方法
10 . 已知函数
,对
且
,恒有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d73c71dc5b43284c70d5476a9d18b95.png)
(1)求
和
的单调区间;
(2)证明:
的图象与
的图象只有一个交点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c96cd9242fddaef9b67eaae24ead52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e401386b7d366e912acc7027cdca8329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d73c71dc5b43284c70d5476a9d18b95.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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