名校
1 . 已知函数
部分图象如图所示.
![](https://img.xkw.com/dksih/QBM/2022/3/30/2947565966606336/2948760817467392/STEM/fb1d5558-38b2-4267-a57a-3484f03ea485.png?resizew=157)
(1)求函数
的解析式;
(2)将函数
的图象向右平移
个单位,再把得到的函数图象横坐标不变,纵坐标变为原来的
,得到函数
的图象.
①求证:方程
上有且只有一个解
;
②若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9600f6b6a61f067a9d62fe31c374b4.png)
![](https://img.xkw.com/dksih/QBM/2022/3/30/2947565966606336/2948760817467392/STEM/fb1d5558-38b2-4267-a57a-3484f03ea485.png?resizew=157)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
①求证:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2dc132aee05b51755b10d01133dc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/954fe0139b7eb82c0baa5317929c8823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f4cfa6abf4f2d4a61da22b969ea641.png)
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2 . 已知函数
的部分图象如图所示.
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897858638028800/2905694596751360/STEM/580f71ea-6ef8-42e3-8919-bea0bc788c86.png?resizew=202)
(1)求函数f(x)的解析式:
(2)证明:
,使得
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ea345085e0957f48cb30766604589c.png)
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897858638028800/2905694596751360/STEM/580f71ea-6ef8-42e3-8919-bea0bc788c86.png?resizew=202)
(1)求函数f(x)的解析式:
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66d64d61aa6daee84d844e1458c009e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce00a50660b3f6071dc14d9b872874e.png)
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2022-01-30更新
|
623次组卷
|
3卷引用:江苏省连云港市2021-2022学年高一上学期期末数学试题
3 . 如图,函数
的图像过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/26f44eb2-78ef-46c1-ae8c-af2b7c17a4d6.png?resizew=269)
(1)求证:
,并写出
的解析式;
(2)指出函数
的单调增区间;
(3)解方程
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb99c6441405726bd58734360911eaeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/26f44eb2-78ef-46c1-ae8c-af2b7c17a4d6.png?resizew=269)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c782473400ca663779f6fe453a1c6e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)指出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776110dbd7aa019e43ec15964b9f8e4c.png)
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名校
4 . 已知定义在
的函数
,对任意
,恒有
成立.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/f9f7abd7-5a13-4b10-a25b-cc19b04b84a6.png?resizew=188)
(1)求证:函数
是周期函数,并求出它的最小正周期T;
(2)若函数
(
,
,
)在一个周期内的图象如图所示,求出
的解析式,写出它的对称轴的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ff4a1f5d3ad9d7668fe555e70b774c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c932cdd38a6e861cc8e1f62dddd7f213.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/f9f7abd7-5a13-4b10-a25b-cc19b04b84a6.png?resizew=188)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec89c3bc454d209007c2b29baeeb3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6af3e2115ce0aaf5b99ac70c4441d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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