1 . 综合与实践:
《函数》复习课后,为加深对函数的认识,刘老师引导同学们对函数
的图象与性质进行探究,过程如下,请完成探究过程:
(1)初步感知
函数
的自变量取值范围是 ;
(2)作出图象
①列表:
填空:
表中
,
;②描点,连线:
在平面直角坐标系
中,描出以上表中各对对应值为坐标的点,根据描出的点,画出该函数的图象;
(3)研究性质
小明观察图象,发现这个图象为双曲线,进一步研究中,小明将函数
转化为
,他判断该函数图象就是反比例函数
通过某种平移转化而来,反比例函数
是中心对称图形,对称中心为
,则函数
的对称中心为 ;
当
时,关于x的方程
有实数解,求
的取值范围.
《函数》复习课后,为加深对函数的认识,刘老师引导同学们对函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100fd3461a4efa35563dd4e58f3f35b9.png)
(1)初步感知
函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100fd3461a4efa35563dd4e58f3f35b9.png)
(2)作出图象
①列表:
![]() | … | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | 0 | 1 | 2 | 3 | 4 | … |
![]() | … | ![]() | ![]() | ![]() | 2 | 3 | 4 | ![]() | 6 | ![]() | ![]() | ![]() | ![]() | 0 | ![]() | ![]() | ![]() | … |
表中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
(3)研究性质
小明观察图象,发现这个图象为双曲线,进一步研究中,小明将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100fd3461a4efa35563dd4e58f3f35b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905bb5be942f3aa3667e5ce1c264c02c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b4f23770747042d68b0fa011762258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b4f23770747042d68b0fa011762258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/430b9c003e6f16136fd9ef43654b2b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100fd3461a4efa35563dd4e58f3f35b9.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6ad6387d592102a743742620eee7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e2b7a3f6812352d127a47f9fcad4b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2卷引用:2024年山东省聊城市莘县中考二模数学试题
2 . 如图1,直线
经过点
,交反比例函数
的图象于点
,点
为第二象限内反比例函数图象上的一个动点.
的表达式;
(2)过点
作
轴交直线
于点
,连接
,
,若
的面积是
面积的
倍,请求出点
坐标;
(3)平面上任意一点
,沿射线
方向平移
个单位长度得到点
,点
怡好在反比例函数
的图象上;
①请写出
点纵坐标
关于
点横坐标x的函数关系式
______;
②定义
,则函数
的最大值为______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240479e45c962e843605c936e903aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d1e4a02f6a99a4b838dcaf9541d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d105b74c40724a7da626e7c42afbf5fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d49c77f27b6b40e1a8d5a1d16cfdf98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7081e041ddf37af292ab559c7a5146a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147de24f071e316b68fd2e78e3c84545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4234cf4d8159f5df0333bcc269ffe099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)平面上任意一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23248e0ebb865b5f143e53338fd4faf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42da28be159399514cc6179a96e34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42da28be159399514cc6179a96e34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d105b74c40724a7da626e7c42afbf5fa.png)
①请写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb0166538e588e5918e07cd065969ec.png)
②定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53047be85b38b82a1daab3787d8c3a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4824fc268035cb5d9ed775c29a8762d.png)
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5卷引用:2024年山东省济南市市中区中考一模数学模拟试题
2024年山东省济南市市中区中考一模数学模拟试题2024年山东省济南市中考数学模拟试题(六)(已下线)重难点02 一次函数与反比例函数综合题(4大题型+满分技巧+限时分层检测)-2024年中考数学【热点·重点·难点】专练(上海专用)福建省泉州市丰泽区泉州市第九中学2023-2024学年八年级下学期期中数学试题数学(泰州卷)-【试题猜想】2024年中考考前最后一卷
3 . 如图,在平面直角坐标系中,一次函数
与反比例函数
的图象在第一象限内交于
和
两点,直线
与
轴相交于点
,连接
.
(2)当
时,请结合函数图象,直接写出关于
的不等式
的解集;
(3)过点
作
平行于
轴,交
于点
,在
轴上是否存在点
,使以点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea927ec42e52550b23414948a796096b.png)
为顶点的四边形是平行四边形?若存在请求出
点坐标,若不存在请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c1972246a0a3d1c987d25205dbdd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110d33e45e286a68582664b8d038ec72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42e598dd62bf7f73beceeedecc66d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5550f83d3d2cd3cbcc6694518ac16dd.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea927ec42e52550b23414948a796096b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b845f9bc59ee0bd65bcb22f66d9e4f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2卷引用:2024年山东省济南市长清区九年级中考第一次模拟考试数学模拟试题
4 . 如图,在平面直角坐标系中,一次函数
的图象与反比例函数
的图象交于点
.当
时,x的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed06ccefffc165f9c77250cd28301d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc4622a5f65ffbece28e09206b0cb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23ee070c818278689bc61da856c96eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f99df1a7b58018125b99578b779342.png)
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2卷引用:2024年山东省枣庄市山亭区中考数学二模试题
5 . 如图,在平面直角坐标系中,反比例函数
的图象经过点
,将点A向左平移2个单位,再向上平移a个单位得到点B,点B恰好落在反比例函数
的图象上,过A,B两点的直线与y轴交于点C.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/6c5d5cb6-bcea-4488-b68a-2f6b6ca663d6.png?resizew=142)
(1)求k的值及点C的坐标;
(2)在y轴上有一点D,连接
,若
的面积是4,求D点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c9940526785ca763da2dfa35e77c934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca38f4cef6e2cb4119a56895ddae09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c9940526785ca763da2dfa35e77c934.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/6c5d5cb6-bcea-4488-b68a-2f6b6ca663d6.png?resizew=142)
(1)求k的值及点C的坐标;
(2)在y轴上有一点D,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a929fca455b19682d2a26ecc302123d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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6 . 如图,在平面直角坐标系中,一次函数
的图象与反比例函数
的图象交于点
,与
轴交于点
,过点
的直线与反比例函数
的图象交于点
.
(1)求此反比例函数的解析式;
(2)若点
的纵坐标为1,求直线
的解析式;
(3)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03517310ea1e913f709753592ac65ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b081a3d49f59c6a96a8afb7511f91875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03517310ea1e913f709753592ac65ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/1/58e8d320-6154-45a7-870c-5cb0bd7f7466.png?resizew=178)
(1)求此反比例函数的解析式;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b40c2b0ab8e1cfe5112d428b4b829f.png)
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7 . 如图,一次函数
的图像与反比例函数
的图像交于A,B两点,与x轴交于点C,与y轴交于点D.已知点
,点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/a8efc4c0-2d1a-4912-b5bf-f0753e87344e.png?resizew=170)
(1)求反比例函数与一次函数的解析式;
(2)点M是反比例函数图像上一点,当
与
的面积相等时,请直接写出点M的横坐标;
(3)将射线
绕点A旋转α度后与双曲线交于另一点Q,若
,请求出点Q的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e136e7637543c8ae92c8dcd55b31924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78eba6f91d97cea1dfd73bae53e7b689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454f1c76b7b390aef0b3c57436b67e5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/a8efc4c0-2d1a-4912-b5bf-f0753e87344e.png?resizew=170)
(1)求反比例函数与一次函数的解析式;
(2)点M是反比例函数图像上一点,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68881c60c4d8296162122ca5958e2bc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372629a8666de1e9bac3e7daadcac7b6.png)
(3)将射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d59142ab797807e560fe8adf63e6ecb.png)
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8 . 如图,已知一次函数
与反比例函数
的图象交于点
,
,与两坐标轴分别交于
,
两点,连接
,
.
的值;
(2)若点
在
轴上,且
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74daa4cfb7d9430b97242769d659136f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f8297bca75733768012232c0780311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9dfd1f9c4a71ac07ae1fb3a737fccb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若点
![](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/afb68aaef1480588ad2c3ed4613d3073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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5卷引用:2024年山东省济宁市部分中学中考数学一模试题
2024年山东省济宁市部分中学中考数学一模试题2023年河南省平顶山市叶县模拟预测数学模拟预测题2024年河南省开封市祥符区九年级中考一模数学试题(已下线)专题02 反比例函数综合应用(五大题型)(题型专练)-2023-2024学年八年级数学下册《知识解读·题型专练》(苏科版)2024年河南省中招重点初中模拟联考(二)数学试题
名校
9 . 如图,直线
与双曲线
交于
、
两点
则当
时,
的取值范围是______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73801c38ac23a0776ec3f627c7a85fe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d105b74c40724a7da626e7c42afbf5fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c51419e22a7b175b686e98d83d373a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79108ad3c8e625a94c97a5295bb1b97f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e1d0f65817ba32a732040518f41440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac67e9a909472ab852d38d2ec66a1e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/4/07a9a36f-6c78-40ba-8827-9b2eec33c391.png?resizew=148)
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2卷引用:2023年山东省泰安市岱岳区山东省泰安第十五中学中考数学模拟预测题
名校
10 . 如图,A、B两点的坐标分别为
,
,将线段AB绕点B逆时针旋转
得到线段
,过点C作
于点D,反比例函数
的图象经过点C,交直线
于E.
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee8c50793afd59e6ab4a2be5a877759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fed700b7a3ab2ee7fbae12507033af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786080c82db1e1d3ec6367397aa63220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb6772cca18f6f1cfb7c961a425c8b2.png)
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4卷引用:山东省聊城市第一实验中学等多校2023-2024学年九年级下学期期中数学试题
山东省聊城市第一实验中学等多校2023-2024学年九年级下学期期中数学试题2024年安徽省马鞍山市第八中学中考一模数学试题(已下线)热点08 图形的变化 (2大考向7种题型+重难通关练+培优争分练)-2024年中考数学【热点·重点·难点】专练(安徽专版)2024年广东省东莞市虎门外语学校中考一模数学试题