1 . 将函数
的图象上所有点的横坐标缩短到原来的
,纵坐标不变,得到
的图象.
(1)求
的解析式与最小正周期;
(2)求
图象的对称中心的坐标;
(3)设函数
,求
在
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a4025a394f30a4f8e7a58c921dbccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2595780da91e1c21306800e7fa7d2fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbae6c61828aa9d7a6a04535831151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45f644764b91e5d01e6f830b50d3942.png)
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2 . 将函数
的图象向左平移
个单位长度,然后把曲线上各点横坐标变为原来的
(纵坐标不变)得到函数
的图像.
(1)求函数
的解析式;
(2)若
,求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0a5133b8460df6c46da0e44051e2a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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名校
解题方法
3 . 已知
,
,
(下面①,②中选择一个作为已知条件,解答问题:
(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.
①
的最大值为
;②
.
注:如果选择①和②分别解答,则按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0be576e1d7cc74520944609fa6534a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd7f03b66f78d94edc5db0c0513f320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b655f8a1de139164fcab57390b798e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)将
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac05736945533bdf5e39720ed25f617.png)
注:如果选择①和②分别解答,则按第一个解答计分.
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4 . 已知函数
,
.
(1)求函数
的最小正周期;
(2)将
的图象向左平移
个单位得到的函数
,求
的单调递减区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230e8a254a0521ca7e9877c24b51d17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)将
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
5 . 已知函数
.
(1)求
的最小正周期
;
(2)将
的图象向左平移
个单位得到函数
,求
的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27cb08679529dce27a3c453f4cbe8ae.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)将
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
6 . 已知函数
.
(1)若
时,
恒成立,求实数
的取值范围;
(2)将函数
的图象的横坐标缩小为原来的
,纵坐标不变,再将其向右平移
个单位,得到函数
的图象.若
,函数
有且仅有4个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c309ced402b72999aff2066b4bfed35.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0a5133b8460df6c46da0e44051e2a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5139cf1b63dfa0a0164dd9cb40f18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)将函数
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d9703ec5eee8074ba7fbe0e899b336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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名校
7 . 已知函数
的图象相邻对称轴之间的距离是
,若将
的图像向右移
个单位,所得函数
为奇函数.
(1)求
的解析式;
(2)若函数
的一个零点为
,且
,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06639527a6fb4cb468839dea5ce722a2.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/821e969a2b4c60ce62abaea67d57b2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40597b245c8b21bb32ac42abba4d310.png)
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名校
解题方法
8 . 已知向量
.设
.
(1)求函数
的表达式,并写出该函数图象对称轴的方程;
(2)将函数
的图象向右平移
个单位,得到函数
的图象,直接写出函数
的表达式;
(3)求关于
的方程
在区间
上的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b5b47f49dafaa3c055744116914b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7aa1233d7a93113281594c41f25c7db.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)求关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa757c82f454fe33f592264a7e4d08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
您最近一年使用:0次
9 . 将函数
的图象上所有的点向左平移
个单位长度得到函数
的图象.求:
(1)
的值;
(2)
的单调递减区间、对称轴方程及对称中心.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af853d2ce30483fafa59ff9583b5da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e960ab40ee6533d55c4eb3303bb4c0.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
10 . 已知函数
.
(1)画出函数
在
上的大致图象;
(2)将函数
的图象向右平移
个长度单位,再将横坐标伸长为原来的2倍,纵坐标不变,得到函数
的图象,求函数
在
上的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5d2c2650a50fcc6fb18c5cfba9d916.png)
(1)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4b61d912f99e5583e7e17cf8fef558.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a41a70c47a5997e675d3166420fc39.png)
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