名校
1 . 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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2024·全国·模拟预测
2 . 若函数
在区间
上至少有两个零点,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b1e5d6737404b5e6166069eb658f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/313b01bdf97cdee0ea014f68d59fe6e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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名校
3 . 如图所示,一个质点在半径为2的圆
上以点
为起始点,沿逆时针方向运动,每3s转一圈.则该质点到
轴的距离
关于时间
的函数解析式是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024高三·全国·专题练习
4 . 已知函数y=g(x)=2sin (4x-
),方程g(x)=
在x∈[
,
]上的根从小到大依次为x1,x2,…,xn,试确定n的值,并求x1+2x2+2x3+…+2xn-1+xn的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4966e5af166b69a0a38a98abf555b6b.png)
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2024高三·全国·专题练习
解题方法
5 . 关于函数
,有下述三个结论:
①
是周期为
的函数;
②
在
单调递增;
③
在
上有三个零点;
其中所有正确结论的编号是__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2ac66c4f103f619fede7f6dae7922d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0b1b34a0cb69bd9e0a4622b6352968.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d6a66a015ddd2a8076f35ed191927.png)
其中所有正确结论的编号是
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解题方法
6 . 已知
,则
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6808c268db93fe1affa8cccffa9390d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 已知直线
和
是函数
图像两条相邻的对称轴.
(1)求
的解析式和单调区间;
(2)保持
图像上各点的纵坐标不变,横坐标变为原来的
倍,得到函数
的图像.若
在区间
恰有两个极值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c6cb0cc172657611e286e7fa669584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4eae5056ae4e4f11c49fe4b1fb67908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f26765b493dcb0cb3ebe4f7ef74c3c6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)保持
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ca7d2fde2a0ab2398185e87db8c4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 已知函数
,周期是
.
(1)求
的解析式及值域;
(2)将
图象上所有点的横坐标扩大到原来的2倍,纵坐标不变,再向左平移
个单位后得到函数
的图象,则当
时,求方程
根的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5de1b7a7daadf2279a3811b69f8121d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(1)求
![](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/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6d68581a66f9ffbf8c082206eb4458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f860566dc9976d4ae63969c358bbdb3d.png)
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名校
9 . 在锐角
中,角A,B,C所对的边分别为a,b,c,已知
.
(1)求角C;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51cdd6ed883ae3e50f1f000ab49a7419.png)
(1)求角C;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2edb07bc94c46d55c484e14e1c56b2.png)
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2024-01-12更新
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1268次组卷
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4卷引用:河南省信阳市信阳高级中学2024届高三上学期第七次大考数学试题
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2024·全国·模拟预测
名校
10 . 已知函数
(
,
,
)的部分图象如图所示,将
的图象向左平移
个单位长度得函数
的图象,若
在
上有两个不同的根
,
(
),则
的值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/1e8eba8b-12ab-48cc-93b3-07511568fad0.png?resizew=181)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fcd3cea5f5e2fe943490dcb65d74c73.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/409b95503e9f597f9f63c65917b330c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18193a0af082779fce72d1d3fe1a6677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23efa380a58dc9663ba06dc249ce721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d711738bd847d4324b786532977c10c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4ce170c8918cf7e4942970c2a1c282.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/1e8eba8b-12ab-48cc-93b3-07511568fad0.png?resizew=181)
A.![]() | B.![]() | C.![]() | D.![]() |
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