在初中阶段的函数学习中,我们经历了列表、描点、连线画函数图象,并结合图象研究函数性质的过程.以下是我们研究函数
性质及其应用的部分过程,请按要求完成下列各小题.
(1)下表是
与
的几组对应值:
=______,
=______,描出
,
两个点,并画出函数图象;
(2)根据函数图象,判断下列关于该函数性质的说法是否正确,正确的在答题卡上相应的括号内打“√",错误的在答题卡上相应的括号内打“×”;
①该函数是轴对称图形,对称轴是
轴;
②该函数在自变量的取值范围内,没有最大值,也没有最小值;
③当
时,
随
的增大而减小;
(3)已知函数
的图象如图所示,结合你所画的函数图象,直接写出关于
的方程
的近似解(保留1位小数,误差不超过0.2).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21538945372062563be45564fbd5d65.png)
(1)下表是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![]() | -6 | -5 | -4 | -3 | -2 | -1 | ![]() | ![]() | 1 | 2 | 3 | 4 | 5 | 6 |
![]() | 0 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63ad41010cf2624ad390ca2dd0a1fd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7fba1029d4cb2b569f55cee4658658.png)
(2)根据函数图象,判断下列关于该函数性质的说法是否正确,正确的在答题卡上相应的括号内打“√",错误的在答题卡上相应的括号内打“×”;
①该函数是轴对称图形,对称轴是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
②该函数在自变量的取值范围内,没有最大值,也没有最小值;
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bd7014d6dd6db0b05263d2043133e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8482e7488a9607afa3bffcfc27ea82d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47126b8977e307e9e301aff6016261ba.png)
![](https://img.xkw.com/dksih/QBM/2020/11/16/2600468079968256/2609919899222016/STEM/8bc19c05-38af-49da-80c4-0c2bb740719b.png)
更新时间:2020-12-08 19:58:32
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相似题推荐
解答题-作图题
|
较难
(0.4)
【推荐1】在平面直角坐标系
中,抛物线
的对称轴是直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7152aea5d046953a8c931571be7c529.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/bdea5717-1e71-4499-b482-c57447b237de.png?resizew=212)
(1)求抛物线的表达式,并在图中画出函数图象;
(2)点
在抛物线上,若
,请直接写出n的取值范围;
(3)设点
为抛物线上的一个动点,当
时,点M关于y轴的对称点形成的图象与直线
有交点,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3bdba11661a5d539b74ab2236b65d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7152aea5d046953a8c931571be7c529.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/bdea5717-1e71-4499-b482-c57447b237de.png?resizew=212)
(1)求抛物线的表达式,并在图中画出函数图象;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb8864b03fbc60467dc2193ccd4fdfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf16d0a4300961ccf34b12fff5de87c.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b37b6e7fe54d7c8cba422c00fec4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870bcb99888b7763620666f98f01a513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea32daf98b2687e682a93914364bd9d.png)
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名校
【推荐2】如图,
是
与弦
所围成的图形的内部的一定点,点
是弦
上一动点,连接
并延长交
于点
,连接
.已知
,设
、
两点间的距离为
,
、
两点间的距离为
,
、
两点间的距离为
,
![](https://img.xkw.com/dksih/QBM/2021/6/1/2733799247052800/2735804884901888/STEM/5caf45df99a249c3a58abea86b8c0bc1.png?resizew=275)
小东根据学习函数的经验,分别对函数
,
随自变量
的变化而变化的规律进行了探究.下面是小东的探究过程,请补充完整:
(1)按照右表中自变量
的值进行取点、画图、测量,分别得到了
,
与
的几组对应值:
其中
______.
(2)如图,函数
的图象已经画出,请在同一平面直角坐标系
中,描出补全后的表中各组数值所对应的点
,并画出函数
的图象;
![](https://img.xkw.com/dksih/QBM/2021/6/1/2733799247052800/2735804884901888/STEM/595aa55fd9e241d0bdaca8e0780ed366.png?resizew=495)
(3)结合函数图象,解决问题:当
为等腰三角形时,
的长度约为______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6747441b260ca043446b5d472fece440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3160fce05b551569b8c7b5de6dd8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38703a1be638e22eb5d06e315fbff406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469490cb0402f8cf5a51a143dd9e124f.png)
![](https://img.xkw.com/dksih/QBM/2021/6/1/2733799247052800/2735804884901888/STEM/5caf45df99a249c3a58abea86b8c0bc1.png?resizew=275)
小东根据学习函数的经验,分别对函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)按照右表中自变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
0 | 1 | 2 | 3 | 4 | 5 | 6 | |
5.6 | 4.7 | 3.8 | 2.7 | 3.2 | 4.4 | ||
5.6 | 5.5 | 5.4 | 5.3 | 5.2 | 4.7 | 4.1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
(2)如图,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8529f413a378df2659f52e946e9a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://img.xkw.com/dksih/QBM/2021/6/1/2733799247052800/2735804884901888/STEM/595aa55fd9e241d0bdaca8e0780ed366.png?resizew=495)
(3)结合函数图象,解决问题:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
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解答题-作图题
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【推荐3】小明结合自己的学习经验,对新函数y=
的解析式、图象、性质及应用进行探究:已知当x=0时,y=2;当x=1时,y=1.
(1)函数解析式探究:根据给定的条件,可以确定由该函数的解析式为: .
(2)函数图象探究:
①根据解析式,补全如表,则m= ,n= .
②根据表中数据,在如图所示的平面直角坐标系中描点,并画出函数图象.
(3)函数性质探究:请你结合函数的解析式及所画图象,写出该函数的一条性质: .
(4)综合应用:已知函数y=|
x﹣
|的图象如图所示,结合你所画的函数图象,直接写出不等式|
x﹣
|≤
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77658f9e9195a3d7a8878e37a691aa5b.png)
(1)函数解析式探究:根据给定的条件,可以确定由该函数的解析式为: .
(2)函数图象探究:
①根据解析式,补全如表,则m= ,n= .
②根据表中数据,在如图所示的平面直角坐标系中描点,并画出函数图象.
x | …… | ﹣4 | ﹣3 | ﹣2 | ﹣1 | ﹣![]() | 0 | ![]() | 1 | 2 | n | 4 | …… |
y | …… | ![]() | ![]() | ![]() | m | ![]() | 2 | ![]() | 1 | ![]() | ![]() | ![]() | …… |
(4)综合应用:已知函数y=|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ab109ec88d6f3d24b2f01ca77e7038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf1ff64281c78fe2b96e8ffb166afd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ab109ec88d6f3d24b2f01ca77e7038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf1ff64281c78fe2b96e8ffb166afd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77658f9e9195a3d7a8878e37a691aa5b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/52ec0ec9-8c65-4241-8190-1d2acad60828.png?resizew=404)
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名校
【推荐1】【阅读材料】
因式分解![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0caa11ca5d0ab27b8e12e21f3923e745.png)
我们在解方程
的过程中,可以利用因式分解的知识,把原方程化为
,可得
或![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abb2301cdf9481e78ce4ac2cf54282e.png)
或![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255ceeecd1951358962fdcdee60a3792.png)
经检验发现
或
是原方程的解.
如图,直线
与反比例函数
的图象交于
,
两点,已知点
的坐标为
,
的面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/43060034-21eb-4c66-9922-f87b807c6180.png?resizew=130)
(1)填空:反比例函数的关系式为______________________;
(2)求直线
的函数关系式;
(3)动点
在
轴上运动,当线段
与
之差最大时,求点
的坐标;
(4)在反比例函数
第三象限的图象上找一点
,使得点
到直线
距离最短,请直接写出点
的坐标.
因式分解
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0caa11ca5d0ab27b8e12e21f3923e745.png)
我们在解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2978dbd202b11f35cd83a29143eb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1bf281a1e6313841af61fef945fa31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9378f4030a56301dfdf892c0b36182b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abb2301cdf9481e78ce4ac2cf54282e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042ce35bf466b92be6b96ecd3a6dff1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255ceeecd1951358962fdcdee60a3792.png)
经检验发现
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255ceeecd1951358962fdcdee60a3792.png)
如图,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b9c8fe0bc3b52f512956502ef27b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924e55493002de028151c4a3cd0cc717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/43060034-21eb-4c66-9922-f87b807c6180.png?resizew=130)
(1)填空:反比例函数的关系式为______________________;
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)动点
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(4)在反比例函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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【推荐2】如图,点P为一次函数
与反比例函数
的图象的交点,点P的纵坐标为4,
轴,垂足为B,一次函数
的图象与x轴交于点A,与y轴交于点C.
(2)点M是反比例函数
的图象上的一点,且在点P的右侧,连接
.
①连接
.若
,求点M的坐标.
②过点M作
于点D,若
,求M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e091cface0c4a22727634eb480562d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74daa4cfb7d9430b97242769d659136f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/465aec2e55491394d6a8bfa3ffb2b833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e091cface0c4a22727634eb480562d6.png)
(2)点M是反比例函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74daa4cfb7d9430b97242769d659136f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
①连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2caaefb77a56b75f122f6071c6e5fa4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d8d6eddce2471cd1115a301c9e9864.png)
②过点M作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ab1da5c82cc462538c39e747192244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd608112369d9a2a75f2902b64f7c99.png)
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