2024·全国·模拟预测
1 . 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
2 . 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
3 . 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
4 . 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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5 . 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
6 . 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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2024·全国·模拟预测
名校
7 . 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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2024·全国·模拟预测
8 . 若函数
的图象与函数
的图象的任意三个连续交点都是一个正三角形的三个顶点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2158fdaf5a5fd6d673903038a1b1289a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316f8f70e09f75fff72573fc9698057d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 从物理学知识可知,图中弹簧振子中的小球相对平衡位置的位移
与时间
(单位:
)的关系符合函数
.从某一时刻开始,用相机的连拍功能给弹簧振子连拍了20张照片.已知连拍的间隔为
,将照片按拍照的时间先后顺序编号,发现仅有第5张、第13张、第17张照片与第1张照片是完全一样的,则小球正好处于平衡位置的所有照片的编号有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/a85022b8-8ed2-4d69-9e7a-c4a408e26126.png?resizew=298)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65502a7ea4d1ce6d6d8c720845c73e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce7de4354c11dc324c1ed5294548e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb0ad78e076260617ca2b287837c422.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/a85022b8-8ed2-4d69-9e7a-c4a408e26126.png?resizew=298)
A.4 | B.6 | C.12 | D.18 |
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解题方法
10 . 将函数
的图象向右平移
个单位长度可以得到函数
的图象,若函数
在区间
内有零点,无最值,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0353de646a03c770d51fc68de92bde06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da2b4a54a0fdb26078aeadccccf845c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a53be970f73061098c18a423d6b3beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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