对于定点
,其中
,我们构造一个经过定点p的“
系函数”:若
时,
;若
时,
.
(1)已知点
,则过点A的“
系函数”为________.
(2)已知点
在第一象限内,且过点
的“
系函数”在
时有整数解,求
的值.
(3)已知点
在直线
的上方,且过点
的“
系函数”在
时,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bb7663c0af6e98741550471bd3d673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eae9ba258299eb489b490594397e23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1132de2e8913dba9c5cc2396ecb09fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25af8a1c65b2ee961a7d284a9c9bcdd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6288927a01219e8c3765c568e123015f.png)
(1)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99ce0fdd3a34df8d5e913b7b9f6f3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defe1255c37316e477577f39db0e2971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50403a452f29c3709ab65c8cc3201d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2222b10f3189590dfa35385970ce40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edf57d1ecdfaf8be1d2087d3e7d3358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
更新时间:2023-09-22 12:52:30
|
相似题推荐
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(0.4)
【推荐1】方格纸中的数学——运算线
【加法线】如图1,作
的加法线,先在横线上找到第一个加数
并作横线的垂线,再在竖线上找到第二个加数
并作竖线的垂线,两条垂线相交于点
,过点
沿小方格对角线作直线
,
与横线相交于点
,则点
在横线上所表示的数为
,则
为
的
号加法线.
号加法线上任一点向横线和竖线作垂直后,垂足在横线与竖线上所表示的数之和为
.
(1)在图②中画出
的
号加法线;
(2)类比画加法线的方法,在图2中画出
的
号减法线.
【换个角度看】
(3)①已知两个数
、
,判断
的
号加法线与
的
号减法线的位置关系并说明理由(可借助图③说理);
轴,竖线为
轴.则
的
号加法线与
的
号减法线所表示的函数表达式分别是 .
【乘法线】
(4)如图④,若
所表示的点为坐标原点,以横线为
轴,竖线为
轴,
与乘数
的积的乘法线
称为
号乘法线.求
号乘法线
的函数表达式;
(5)某校数学社团男同学比女同学多
人,且男同学人数是女同学人数的
倍,在图⑤中,利用运算线求男同学的人数.
(6)
号乘法线(
为常数,
)上任一点的函数值与
差的
号减法线和
的
号加法线.当
时,
.结合图像,直接写出k的取值范围.
【加法线】如图1,作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c270b42796c0741762931bb17dcb2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79c562343bd2362a979662d3865020c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c270b42796c0741762931bb17dcb2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79c562343bd2362a979662d3865020c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79c562343bd2362a979662d3865020c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79c562343bd2362a979662d3865020c.png)
(1)在图②中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff46d3dbbcc33795311c36e609db45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
(2)类比画加法线的方法,在图2中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37681799e0f01a2064597f5bee25bdeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
【换个角度看】
(3)①已知两个数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79c562343bd2362a979662d3865020c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d6df06a5b85848dc4fa33327f8e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79c562343bd2362a979662d3865020c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d6df06a5b85848dc4fa33327f8e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
【乘法线】
(4)如图④,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(5)某校数学社团男同学比女同学多
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(6)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a2a6ca02246d7bbb3207927eb62a7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200849ce71f53c0321506e27de437b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1113e9b568fb9ca3286582368e257a.png)
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【推荐2】因为疫情,体育中考中考生进入考点需检测体温.防疫部门为了解学生错峰进入考点进行体温检测的情况,调查了一所学校某天上午考生进入考点的累计人数y(人)与时间x(分钟)的变化情况,数据如下:
(1)研究表中数据发现9分钟内考生进入考点的累计人数是时间的二次函数,请求出9分钟内y与x之间的函数关系式.
(2)如果考生一进考点就开始排队测量体温,体温检测点有2个,每个检测点每分钟检测20人,求排队人数最多时有多少人?全部考生都完成体温检测需要多少时间?
(3)在(2)的条件下,如果要在12分钟内让全部考生完成体温检测,从一开始就应该至少增加几个检测点?
时间x(分钟) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
人数y(人) | 0 | 170 | 320 | 450 | 560 | 650 | 720 | 770 | 800 | 810 | 810 |
(2)如果考生一进考点就开始排队测量体温,体温检测点有2个,每个检测点每分钟检测20人,求排队人数最多时有多少人?全部考生都完成体温检测需要多少时间?
(3)在(2)的条件下,如果要在12分钟内让全部考生完成体温检测,从一开始就应该至少增加几个检测点?
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【推荐3】某景区今年对门票价格进行动态管理.节假日期间,10人以下(包括10人)不打折,10人以上超过10人的部分打折;非节假日期间全部打折.设游客为x人,非节假日门票费用y1(元)及节假日门票费用y2(元)与游客x(人)之间的函数关系如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/4cbaf38f-56d9-4845-b1ba-56ae172bd5de.png?resizew=149)
(1)求不打折的门票价格;
(2)求y1、y2与x之间的函数关系式;
(3)导游小王5月2日(五一假日)带A旅游团,5月8日(非节假日)带B旅游团到该景区旅游,两团共计50人,两次共付门票费用3040元,求A、B两个旅游团各多少人?(温馨提示:节假日的折扣与非节假日的折扣不同)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/4cbaf38f-56d9-4845-b1ba-56ae172bd5de.png?resizew=149)
(1)求不打折的门票价格;
(2)求y1、y2与x之间的函数关系式;
(3)导游小王5月2日(五一假日)带A旅游团,5月8日(非节假日)带B旅游团到该景区旅游,两团共计50人,两次共付门票费用3040元,求A、B两个旅游团各多少人?(温馨提示:节假日的折扣与非节假日的折扣不同)
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【推荐1】已知,抛物线
与x轴交于
和
两点,与y轴交于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e66c147f4740fe5e83ba57caa88891b.png)
![](https://img.xkw.com/dksih/QBM/2012/1/8/1573327105318912/1573327251980288/STEM/4c6103ae74094371adc25c3e68cb3b50.png?resizew=174)
(1) 求这条抛物线的解析式和抛物线顶点M的坐标
(2) 求四边形ABMC的面积;
(3)在对称轴的右侧的抛物线上是否存在点P,使
为直角三角形?若存在,求出所有符合条件的点P的坐标,若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83f2638d71e5d00c241c6704b32094d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8333029443d2e3400033ed4da5bffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed5bca4c52cd7505cf92d3c7f6058e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e66c147f4740fe5e83ba57caa88891b.png)
![](https://img.xkw.com/dksih/QBM/2012/1/8/1573327105318912/1573327251980288/STEM/4c6103ae74094371adc25c3e68cb3b50.png?resizew=174)
(1) 求这条抛物线的解析式和抛物线顶点M的坐标
(2) 求四边形ABMC的面积;
(3)在对称轴的右侧的抛物线上是否存在点P,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3be3e9442e707868d3edb2d1bc84e3.png)
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名校
【推荐2】定义:用一条直线截三角形的两边,若所截得的四边形对角互补,则称该直线为三角形第三条边的“幸福线”.如图1,
为
的截线,截得四边形
,若
,则称
为
边
的“幸福线”.
为
边的“幸福线”,
,
,
,求
的长;
(2)如图2,若
内接于
,
为弧
的中点,
、
分别为
、
边的“幸福线",求证:
;
,
,如图3过
点作
的“幸福线”
交
于点
,当四边形
面积最大时,求
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c42bce098904b241986bb91c65ab33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2121f7587818ad20cc350251563b4d71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb3d1070981fed5ca65a34bb2282e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad4c0ba3a6750537789844d0ec419d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69baaff0b38cac0e000c64f72d75336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b939af5ba06e279cce39396aaf0fae06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72d8a3dc6cb93171ee20567b5440775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb8eca20ce2c918ea4034ea15210c7f.png)
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较难
(0.4)
【推荐3】如图是某隧道截面示意图,它是由抛物线和长方形构成,已知OA=12米,OB=4米,抛物线顶点D到地面OA的垂直距离为10米,以OA所在直线为x轴,以OB所在直线为y轴建立直角坐标系.
(1)求抛物线的解析式;
(2)由于隧道较长,需要在抛物线型拱壁上需要安装两排灯,使它们到地面的高度相同,如果灯离地面的高度不超过8米,那么两排灯的水平距离最小是多少米?
(3)一辆特殊货运汽车载着一个长方体集装箱,集装箱宽为4m,最高处与地面距离为6m,隧道内设双向行车道,双向行车道间隔距离为0.5m,交通部门规定,车载货物顶部距离隧道壁的竖直距离不少于0.5m,才能安全通行,问这辆特殊货车能否安全通过隧道?
(1)求抛物线的解析式;
(2)由于隧道较长,需要在抛物线型拱壁上需要安装两排灯,使它们到地面的高度相同,如果灯离地面的高度不超过8米,那么两排灯的水平距离最小是多少米?
(3)一辆特殊货运汽车载着一个长方体集装箱,集装箱宽为4m,最高处与地面距离为6m,隧道内设双向行车道,双向行车道间隔距离为0.5m,交通部门规定,车载货物顶部距离隧道壁的竖直距离不少于0.5m,才能安全通行,问这辆特殊货车能否安全通过隧道?
![](https://img.xkw.com/dksih/QBM/2019/4/26/2190909816823808/2198038973767680/STEM/c4a99b0f33c845748d959118c3c91ae0.png?resizew=183)
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