1 . 已知函数
.
(1)请用“五点法”画出函数
在一个周期
上的简图;
(2)请说明由
到
的变换过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d611f7b20cfdfb3c0ab97882cbe798.png)
(1)请用“五点法”画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80159cf12332e782c46d1aff3866e559.png)
(2)请说明由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588bbf780d49cf4d29802c2e4126f112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2 . 从某企业生产的某批次产品中抽取100件,测量这些产品的一项质量指标值,由测量表得如下频数分布表:
(1)在答题卡上作出这些数据的频率分布直方图:
(3)在某批次产品的抽检中,若出现了质量指标值在
(
为样本平均数,
为样本标准差)之外的产品,则认为该批次产品的生产过程可能出现了异常情况,需对该批次产品的生产过程进行检查.试问该企业是否需对本批次产品的生产过程进行检查?
质量指标值分组 | ![]() | ![]() | ![]() | ![]() | ![]() |
频数 | 6 | 28 | 34 | 24 | 8 |
(1)在答题卡上作出这些数据的频率分布直方图:
(3)在某批次产品的抽检中,若出现了质量指标值在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cbc1ee03729598dd079e9255428e80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
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3 . 在四棱锥
中,底面
为直角梯形,
,
,
,三棱锥
的体积为
,平面
与平面
的交线为
.
的体积,并在答卷上画出交线
(注意保留作图痕迹);
(2)若
,
,且平面
平面
,在
上是否存在点
,使平面
与平面
所成角的余弦值为
?若存在,求
的长度;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b183492677d0457b8701c53d9fa1414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0041488020a3e19377b18a70fbf82e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b2d2f8eb476a313b02f90b71bf8b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
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4 . 已知函数
的最小正周期为
.
(1)求
的单调递增区间;
(2)用“五点法”,列表画出函数
在一个周期上的图象;
图象经过怎样的变换,可以得到
的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3a9c4a0c6ca907debc2e567f7c605a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)用“五点法”,列表画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c85eb9844b07eb3a79142c3aa6f236.png)
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5 . 已知函数
满足
.
的值;
(2)用五点法画出函数
在一个周期上的图象;
(3)根据(2)得到的图形,写出函数
的图象的对称轴方程与对称中心的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04108128425158e44c62533b7fbbae4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7966f0740c2827c8403ac6aa8c371b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)用五点法画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)根据(2)得到的图形,写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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6 . 已知函数 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39b12403fda55a20620a51d864ecd4e.png)
(1)试用“五点法”画出函数
在区间
的简图;
(2)若
时,函数
的最小值为
,试求出函数
的最大值并指出
取何值时,函数
取得最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39b12403fda55a20620a51d864ecd4e.png)
(1)试用“五点法”画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bcab30f6839d1a4427ce179b55d72c2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4420ba6bf7666c8293e59debcc6e8bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a526208da27d53bae502442a92285b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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7 . 已知函数
.
(1)完成上面表格,并用“五点法”作函数
在
上的简图;
(2)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c30682b27a6ecf5f145fc66f3669129.png)
0 | |||||
(1)完成上面表格,并用“五点法”作函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f96a23757dc485b91a6b78b496922b3.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bdabb491742b76e6b880a1d734f0353.png)
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解题方法
8 . 已知函数
.
在
上的图象;
(2)写出
的解集;
(3)把
图象向右平移
个单位长度,再将图象上所有点横坐标缩短为原来
(纵坐标不变),得到
的图象,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66931c1273b2db867d41149e1fb3a8b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c195698ac387fe53b3b1e0248a1fcc92.png)
![]() | ![]() | ![]() | ||||
![]() | 0 | ![]() | ||||
![]() |
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(3)把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66931c1273b2db867d41149e1fb3a8b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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9 . 已知函数
.
(1)求当
取得最大值时,
的取值集合;
(2)求
在
上的值域.
(3)完成下列表格并在给定的坐标系中,画出函数
在
上的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263b6515dcf00962f33ba153be3969e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/1d0924a3-bb66-489f-92f7-dc57e7b811c8.png?resizew=161)
(1)求当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7466d2055b1e49baea19e7e13cf97b77.png)
(3)完成下列表格并在给定的坐标系中,画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
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解题方法
10 . 已知函数
.
(1)求函数
的最大值和最小值及相应自变量x的取值集合;
(2)画出函数
在区间
上的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aecc8f25ff5e382a7e5e62fe9b606f0.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
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