解题方法
1 . 已知定义在R上的奇函数
,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/a17a9948-6bf6-4aa1-b935-475ffba8ce10.png?resizew=156)
(1)在给出的坐标系中画出
的图象(网格小正方形的边长为1);
(2)求函数
在R上的解析式,并写出函数
的值域及单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15308be822e4af7bc4054e7aa4c50e80.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/a17a9948-6bf6-4aa1-b935-475ffba8ce10.png?resizew=156)
(1)在给出的坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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名校
解题方法
2 . 已知函数
,
,其中常数
.
(1)当
时,写出函数
的单调区间(无需证明);
(2)当
时,方程
有四个不相等的实根
.
①求
的乘积;
②是否存在实数
,使得函数
在区间
单调,且
的取值范围为
,若存在,求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528c47af5e756030df86aef0798acc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
②是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e333c856d24ba160c4623cbe335ca4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8af7bed124f00c8e19b52d028b4d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
3 . 已知函数
是奇函数,当
时,
.
(1)求
的解析式;
(2)判断函数
的单调性;
(3)若方程
有三个不同的根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8672676e9dd12438f37584512c6380c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be315e528951120e7d551f654d2a1f5e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
4 . 已知函数
.
(1)当
时,求
的单调区间![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若函数
的定义域内存在
,使得
成立,则称
为局部对称函数,其中
为函数
的局部对称点,若
是函数
的局部对称点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed043ef226eeb5aec48271343dd27b4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328c68de7e5b0204ffd6e8a265ce61a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-01-27更新
|
296次组卷
|
2卷引用:浙江省温州市2023-2024学年高一上学期期末教学质量统一检测数学试题(B卷)
解题方法
5 . 已知定义在
上的奇函数
,当
时
.
(1)求函数
的表达式;
(2)请画出函数
的图象;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/13/5d1f99d4-80cc-44d0-87a7-88b47fbd57b0.png?resizew=205)
(3)写出函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c038bc48671118df97d0e4938fe4ab90.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)请画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/13/5d1f99d4-80cc-44d0-87a7-88b47fbd57b0.png?resizew=205)
(3)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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名校
6 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/38a3e07b-1c8e-4231-9420-cc17420e4992.png?resizew=167)
(1)画出函数图象,并写出函数的值域;
(2)求使函数
有两个不同的零点时的n的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ac01ec3306e0f5f2b80b86bee20bed.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/38a3e07b-1c8e-4231-9420-cc17420e4992.png?resizew=167)
(1)画出函数图象,并写出函数的值域;
(2)求使函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684ba4e6561428d093a1b18f1dca7ce0.png)
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解题方法
7 . 已知
是
上的奇函数,且当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/52d38c14-7d26-48c7-9e2d-4ff5e11c23b6.png?resizew=189)
(1)求
;
(2)求
的解析式;
(3)画出
的图象,并指出
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f26ccb55fcd29bbbacb32598b852910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/52d38c14-7d26-48c7-9e2d-4ff5e11c23b6.png?resizew=189)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a57e7e65245a4d173c5d0bc3c34e45.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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8 . 已知函数
(其中
),且
,
.
(1)求
,
的值;
(2)求
的单调区间;
(3)若正实数
,
满足
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64527c19df5c1d45128d4d26c4a886be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1d97c42f236c05bd0f97ee6538ea61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b49cf13331c53446d9082db8734157.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d900314efb0e4cacb6e5de945b5397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3ecbbaca8eeb1cfa8f4035f7d5726.png)
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解题方法
9 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
时,求函数
的单调区间;
(2)若函数在
内为增函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c23a181a8308c0215a09ef2925abb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da331b83b4d66da80cc3c4fdc38eabfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
10 . 如图,定义在
上的函数
的图象由一条线段及抛物线的一部分组成.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/32cd8c06-fa1c-4237-816c-f469ea6de0c6.png?resizew=176)
(1)求
的解析式;
(2)指出
的单调区间;
(3)直接写出
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ca5e984d5e14b4be18a5ee99f80a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/32cd8c06-fa1c-4237-816c-f469ea6de0c6.png?resizew=176)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)指出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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