1 . 已知函数
的图象相邻对称轴之间的距离是
,若将
的图象向右移
个单位,所得函数
为奇函数.
(1)求
的解析式;
(2)若函数
的零点为
,求
;
(3)若对任意
,
有解,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f26765b493dcb0cb3ebe4f7ef74c3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e8802209a7f2829dfd991a2a3e023c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0383d1373d62a9529b8cd1d79e718af6.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec5d200b561e4be52ccaaebdc3105d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82fd455bee07f28727e234615a0caa6.png)
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名校
2 . 函数
(其中
)的部分图像如图所示,把函数
的图像向右平移
个单位,得到函数
的图像.
时,求函数
的解析式;
(2)对于
,是否总存在唯一的实数
,使得
成立?若存在,求出实数
的值或取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8665842489bc1b588fa43d34730fd1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14fd82a003d2169031a410c5aa7cce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3202accc07b0e7f89091597a7f93684e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e9d00c80b1832b5c6c1085044353b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf143f9bdbbd46200d3e5a244e28573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e1ce7071be0743ded4a087fd908eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
3 . 已知函数
,若把
的图象上每个点的横坐标缩短为原来的
倍后,再将图象向右平移
个单位,可以得到
.
(1)求函数
的周期和解析式;
(2)求
在
上的值域;
(3)若
在区间
上有5个不同的解,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5b1f8c1dfdfeaa77fe7004201403b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b129d5bd03bd4e3895dcb15bec8eedf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8fa4cd0822ad07ef0d2af24428ab9ff.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6547672c4d5ec67b6a3cf1b0eb0818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
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4 . 将函数
图象上所有点的横坐标缩短为原来的
,纵坐标不变,再将所得函数的图象向右平移
个单位长度,最后将所得函数的图象上所有点的纵坐标伸长为原来的2倍,横坐标不变,得到函数
的图象.
(1)求
的解析式,并写出其振幅,最小正周期和初相;
(2)求
的最值以及取得最值时
的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ac3e1432957734d372d8485fb84de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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解题方法
5 . 已知函数
的部分图象如图所示.
的解析式;
(2)将函数
的图象上所有点向右平移
个单位,再将所得图象上每一个点的横坐标变为原来的
倍(纵坐标不变),得到函数
的图象在
时,恰有一个最大值和一个最小值,求
的范围;
(3)若
对任意
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410e99a49e3982ddc82608b54992eedf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c0f4f6ded0865a4364d4cc7b70dce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbb01a7f5e9861aa185c6c63fcd58c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34ca4e9a53e49f06b4583f561098cd0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8065970f190e08a6ce178f765560554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe276c0522839b1d37086d92612aa7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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6 . 已知函数
.
内的图象(要求先列表后描点连线);
(2)
,求
的值;
(3)将函数
的图象向左平移
个单位长度,再将横坐标伸长为原来的2倍,得到函数
的图象,求
的单调增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fb5d5829acb56f74045aaafa0fc56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/261f998fc8fcf7da2931205de40cd6d4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c80daa335a674dabcfefd05022a6abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9454dd0dc83f8e251a0a1722cca9ec51.png)
(3)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
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7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0863c43644cc1d61155def7298902dfd.png)
,
的最大值为
.
(1)求
的值;
(2)将
的图象向右平移
个单位得到
的图象,求函数
的单调增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0863c43644cc1d61155def7298902dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf8197e4f3fd18815045d29c357a863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
您最近一年使用:0次
8 . 已知函数
,将
的图象上所有点的横坐标扩大为原来的
倍(纵坐标不变)得到
的图象.
(1)求
的单调递增区间;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8c7a750ff4705464c01eff2651d00e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be1bad7c22c38c8cf89ff66ad7597ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff09d4a7d482547c2e45060a4f7311a5.png)
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名校
9 . 函数
的部分图象如图所示,
(1)求函数
的解析式和单调递增区间;
(2)将函数
的图象上的各点的纵坐标保持不变,横坐标伸长为原来的2倍,得到函数
的图象,若
时,
的图象与直线
恰有三个公共点,记三个公共点的横坐标分别为
且
,求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca52e9b681b6b8fd19963644cb648080.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/9/2df43a9b-4f3d-4642-9bab-74bf582f1910.png?resizew=161)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)将函数
![](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/3dd5b50eca92d9948792c4bfe9e7991f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a10c3b431d95bb70bacd0a793d5582.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/ab480ea5d44a70a89cbc6a06c922e63e.png)
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名校
解题方法
10 . 已知函数
的部分图象如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/02003ac1-6ea6-4cb6-bd19-cabdff0c6589.png?resizew=174)
(1)求函数
的解析式及其单调递增区间;
(2)将函数
的图象上所有的点向右平移
个单位,再将所得图象上每一个点的横坐标变为原来的2倍(纵坐标不变),得到函数
的图象.若方程
在
上有三个不相等的实数根
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae25bd1441858f763b0fda22bdb139e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/02003ac1-6ea6-4cb6-bd19-cabdff0c6589.png?resizew=174)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a09da1efd0f599dd4682f2284822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a604fadcbf8568cbd8dacddd68443e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f2c9ba604e34100159eb10cccd2b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a8516b1db6979a28b07fd841c7f06b.png)
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