如图,在平面直角坐标系中,一次函数
的图象与正比例函数
的图象交于点
.
(2)设一次函数
的图象与x轴交于点B,与y轴交于点C,求点B,点C的坐标;
(3)写出使函数
的值小于函数
的值的自变量x的取值范围;
(4)在x轴上是否存在点P使
为等腰三角形,若存在,请直接写出点P的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d67d534b258dc1774320f6138f486a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7742e18d0d1458c4837195ecda64db06.png)
(2)设一次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d67d534b258dc1774320f6138f486a.png)
(3)写出使函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d67d534b258dc1774320f6138f486a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
(4)在x轴上是否存在点P使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
20-21八年级上·甘肃酒泉·期末 查看更多[11]
甘肃省酒泉市肃州区第六片区2020-2021学年八年级上学期期末数学试题河北省保定师范附属学校2020-2021学年下学期期中检测八年级数学试题新疆维吾尔自治区塔城地区乌苏市2020-2021学年八年级下学期期末数学试题四川省遂宁市射洪市2021-2022学年八年级上学期期末数学试题(已下线)专题2.7 一元一次不等式与一次函数(知识讲解)-2022-2023学年八年级数学下册基础知识专项讲练(北师大版)(已下线)专题2.9 一元一次不等式与一次函数(巩固篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(北师大版)(已下线)第4课时 一次函数的应用-2022-2023学年八年级数学下册同步考点知识清单+例题讲解+课后练习(人教版)2023年河北省秦皇岛市开发区中考二模数学试题2023年河北省秦皇岛市中考二模数学试题(已下线)2023年河北中考数学二模一次函数图象、性质、探究题2023年河北省邯郸市第十三中学中考二模数学试题
更新时间:2023-05-22 08:31:09
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相似题推荐
解答题-问答题
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适中
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【推荐1】如图 1, 抛物线
与x轴交于点 A、
, 与y轴交于点
,点P是抛物线上一个动点,且在直线
的上方.
(2)当
的面积为8时,请求出点P的坐标;
(3)
能否为直角三角形?若能,请求出此时点P 的坐标;若不能,请说明理由;
(4)如图2,点H的坐标是
, 点Q为x轴负半轴上一动点,点
在抛物线上,把
沿
翻折,使点 P刚好落在x轴上,请直接写出点 Q 的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96dde9c4aad0536c069127df0d4b12f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf982e2547498e78cd6b95f5bcaaa62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f250188b1e44d34509aa13c3f4c5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
(4)如图2,点H的坐标是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0486cb10e2bfa9055fc0333195a08cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0adee0943d128205d6d55cc5dc855187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72f02ad5ced321b7fcc960742533a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c018b37259f3ead2ab2d94bd744f44d.png)
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【推荐2】某商家购进一批产品,成本为10元/件,现有线上和线下两种销售方式,售价均为x元/件(
).调查发现,线上的销售量为600件;线下的销售量
(单位:件)与售价
(单位:元/件)满足一次函数关系,部分数据如表:
(1)求y与x的函数关系式;
(2)求当售价为多少元时,线上销售利润与线下销售利润相等;
(3)若商家准备从线上和线下两种销售方式中选一种,怎样选择才能使所获利润较大.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e137b7421a9d1a98661a86645ee0e6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
x(元/件) | 12 | 13 | 14 | 15 | 16 |
y(件) | 1200 | 1100 | 1000 | 900 | 800 |
(2)求当售价为多少元时,线上销售利润与线下销售利润相等;
(3)若商家准备从线上和线下两种销售方式中选一种,怎样选择才能使所获利润较大.
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【推荐3】在平面直角坐标系
中,O为原点,对于两个图形
和直线
,若在图形X上存在点A,在图形Y上存在点B,使得点A和点B关于直线
对称,就称图形X和Y互为m关联图形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/dd5f86b6-0a41-494c-9787-52ce008cefc9.png?resizew=142)
(1)已知点P的坐标为
,
①点P与点Q互为
关联图形,则点Q的坐标为 ;
②若
的半径为1,点P与
互为m关联图形,则m的值为 ;
(2)已知点
,射线OA与线段l:
互为t关联图形,求t的取值范围.
(3)已知⊙O的半径为2,直线
与x轴,y轴分别交于C,D,若
关于
对称的图形S与点C互为2m关联图形,直接写出m的值及点D与图形S的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7b379a7ebfe72cd64a4ab82794f794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/dd5f86b6-0a41-494c-9787-52ce008cefc9.png?resizew=142)
(1)已知点P的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44e9121523333fd108430ef5ea87058.png)
①点P与点Q互为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1b11762776eb9925bd6b7706b788b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0e6a3764cd3665b3155a8d1ec6aa2e.png)
(3)已知⊙O的半径为2,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6fc0da4f7703cf4692b9a5e2a3412f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
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【推荐1】已知一次函数
的图象过点
,且与一次函数
的图象相交于点
.
(1)求点
的坐标和函数
的解析式;
(2)在平面直角坐标系中画出
,
的函数图象;
(3)结合你所画的函数图象,直接写出不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/197d37a322f0754e556e7b03e1d4e9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa71aa2ea224669698850108751a71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7050d4cdb3485d9e88a80777e5b7cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa2cc17a254cd190ee5bd4d600870a1.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
(2)在平面直角坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
(3)结合你所画的函数图象,直接写出不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60149a3a6af016dda9551559e6da2e96.png)
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【推荐2】如图,直线
:
交x轴于点B,与过点
的直线
:
交于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcddd9b0689eceec5d503240facee044.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/6/7aabebf2-6f76-4c65-bcf4-15303bf16140.png?resizew=281)
(1)求直线
的解析式,并画出
的图象;
(2)求
的面积;
(3)根据函数图象,直接写出
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48eda4f9218b55fbb01201a1a383c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c4f9bdae1190d17d572603937a63aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8578000985b74cbcaa3de6e14cb26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcddd9b0689eceec5d503240facee044.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/6/7aabebf2-6f76-4c65-bcf4-15303bf16140.png?resizew=281)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)根据函数图象,直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47253566c367f4e04cf9128ec27ef40d.png)
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【推荐3】探究函数性质时,我们经历了列表、描点、连线画出函数图象,观察分析图象特征,概括函数性质的过程.结合已有的学习经验,画出函数
的图象并探究该函数性质.
![](https://img.xkw.com/dksih/QBM/2022/5/30/2990564647526400/2991302924804096/STEM/1a673ff3-307e-4c97-b0c4-08ca7941658e.png?resizew=284)
(1)列表,写出表中
,
的值:
______,
______;
在所给的平面直角坐标系中画出该函数的图象.
(2)观察函数
的图象,写出该函数的两条性质:
①______________________________
②______________________________
(3)已知函数
的图象如图所示,结合你所画的函数图象,直接写出不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f240259d5bc34f48622a6cfab084418.png)
![](https://img.xkw.com/dksih/QBM/2022/5/30/2990564647526400/2991302924804096/STEM/1a673ff3-307e-4c97-b0c4-08ca7941658e.png?resizew=284)
(1)列表,写出表中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![]() | … | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | … |
![]() | … | ![]() | ![]() | -2 | -4 | ![]() | -4 | -2 | ![]() | ![]() | … |
(2)观察函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f240259d5bc34f48622a6cfab084418.png)
①______________________________
②______________________________
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf604f85f0d6b273677c6e360e4a23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c2471e42cf5d0265bfb2db420f5d46.png)
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【推荐1】如图,直线
与
轴交于点
,与
轴交于点
,把△
沿着过点
的某条直线折叠,使点
落在
轴负半轴上的点
处,折痕与
轴交于点
.
![](https://img.xkw.com/dksih/QBM/2021/2/7/2652804250296320/2652909617250304/STEM/f07a84d5-57b2-49f8-8e87-1f5f6866ccc5.png?resizew=174)
(1)试求点
、
、
的坐标;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b098e17fa76c648424e9cadf558cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.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/d053b14c8588eee2acbbe44fc37a6886.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2021/2/7/2652804250296320/2652909617250304/STEM/f07a84d5-57b2-49f8-8e87-1f5f6866ccc5.png?resizew=174)
(1)试求点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45c8c0c559b3982a758298020bf7f74.png)
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【推荐2】如图,直线l1:y=x+3与过点A(3,0)的直线l2交于点C(1,m),与x轴交于点B.
(1)求m的值以及直线l2的解析式;
(2)点M在直线l1上,MN∥y轴,交直线l2于点N,若MN=AB,求点M的坐标.
(1)求m的值以及直线l2的解析式;
(2)点M在直线l1上,MN∥y轴,交直线l2于点N,若MN=AB,求点M的坐标.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/fc73bf63-431b-4bad-a654-8761076515f0.png?resizew=245)
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【推荐1】在平面直角坐标系
中,已知直线
(
为常数)与双曲线
交于
两点,且线段
的长度等于5,求常数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a9e1eb4c3226489d1344321b10b7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13653a89d3a38346e1ddf4fd1602f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef854dfcbba9b7dedc1bc52f6332b011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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【推荐2】探究一:在平面直角坐标系中探究
的几何意义
例如:已知
,
,如果要求
、
两点之间的距离,可以构造如图
所示的直角三角形,则
、
之间的距离为______.
结论:在平面直角坐标系中,已知平面内
、
两点坐标,则
、
两点之间的距离等于
因此,
的几何意义可以理解为点
与点
之间的距离
.
应用一:
的几何意义可以理解为点
与点
______,______
的距离和点
与点
______,______
的距离之和.
![](https://img.xkw.com/dksih/QBM/2022/12/27/3139985936080896/3153448471306240/STEM/1109293d6dd94183af80a1e095fbeab4.png?resizew=412)
探究二:求代数式
的最小值.
解:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b642c24d765df93f03fe48de26498c0.png)
如图
,建立平面直角坐标系,点
是
轴上一点,则
可以看成
与点
______,______
的距离.
可以看成点
与点
______,______
的距离.
所以原代数式的值可以看成线段
与
的长度之和,
的最小值就是原代数式的最小值,设点
关于
轴的对称点为
,则
,因此求
的最小值,只需求
的最小值.而点
、
之间的所有连线中线段最短,所以
的最小值为线段
的长度.为此,构造直角三角形
,所以
______.
即
的最小值为______.
拓展:代数式
的最小值为______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55274048f2730cd0d3127bbaeee48e5.png)
例如:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f1f2b3e349a9be5fb156ae31525b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dbd1ebb13ad4c3fc0df396f2842cede.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/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
结论:在平面直角坐标系中,已知平面内
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.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/732e56190d0590e5727614dd4f86b9ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55274048f2730cd0d3127bbaeee48e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f109ad046f362d8686c7ef9810c568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a388a8e291afb1c37d0faee69dee2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
应用一:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a08f5979f8d4c9e9b200b2af02eb08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f109ad046f362d8686c7ef9810c568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8a65fcb0beeca45f72f11e23a1d182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f109ad046f362d8686c7ef9810c568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff1c7b67fe42508d5bd2fd9a3e42788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://img.xkw.com/dksih/QBM/2022/12/27/3139985936080896/3153448471306240/STEM/1109293d6dd94183af80a1e095fbeab4.png?resizew=412)
探究二:求代数式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e14cdfb0a6a24bf39a73f62c0aa6ff.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b642c24d765df93f03fe48de26498c0.png)
如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d93b24dee2e45c97967316a0ac21ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306c3d278c5de624cb1ff36dd13fd7f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d93b24dee2e45c97967316a0ac21ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2118e5d9ce2fb68b4d2970176ff79251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6358468580950fb0903827a4ed0ee1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d93b24dee2e45c97967316a0ac21ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a920a78c48e71749017d40e01caa3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
所以原代数式的值可以看成线段
![](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/a13ec9a812274ad0839f20ba17348687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d7ffb7889a31b267a85f1ea238138e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71cac31d3658b91b471dd109a8bb7018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13ec9a812274ad0839f20ba17348687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0bd62c56cad3d046489cbacc997c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d7ffb7889a31b267a85f1ea238138e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0bd62c56cad3d046489cbacc997c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9806df6df27bf715c81c4a93fc6517c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16f4d5606264224f6357b6adc08396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80327709b35bcf7a86f970984e1b61ab.png)
即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e14cdfb0a6a24bf39a73f62c0aa6ff.png)
拓展:代数式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29167588eb94a41950a3dc73aec2f4c.png)
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