1 . 对于两个一次函数
,
,我们称一次函数
为这两个函数的复合函数.
(1)一次函数
与
的复合函数为______;
(2)若一次函数
,
的复合函数为
,则
______,
_______;
(3)已知一次函数
与
的复合函数的图像经过第一、三、四象限,常数
、
满足的条件是
_______,
______;
(4)若
,一次函数
与
的复合函数的图像是否经过定点?如果是,求出其坐标;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0864e58795cf23b9e877117f0e642b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2023af86eb4901d0373c1b7ec1c2088f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31a16d0480c4d13ce1c78349766e5dd.png)
(1)一次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fd29de0fca59ca8e1db0c0bff8c35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8652faaf1560a7914b30fe8c3d7a7c67.png)
(2)若一次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231896d2386c924306fce5ccf9f9e8a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13653a89d3a38346e1ddf4fd1602f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e003f1d9709a5d9eed462b00cf815101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(3)已知一次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccd9b4b93984c47dbc074ed3da0a488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7d3dd8fac0e4140b4efea436750cfe.png)
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9443c486c23d6a5a4ad1cd7b6a766446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccd9b4b93984c47dbc074ed3da0a488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9124b7978fe55096f16e8686c726ddef.png)
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2 . 数轴上有三个点
,分别代表的整数是
,点
在数轴上的位置如图,
,
满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/5c91d3ab-1747-42a3-bf10-893f4d74960c.png?resizew=362)
(1)
______,
______,
______,点
与点
之间的距离是______;
(2)点A以每秒2个单位长度的速度向左运动,点
以每秒4个单位长度的速度向左运动,点
以每秒
个单位长度的速度向右运动,点
同时运动,设运动时间为
秒,回答下列问题:
①
秒时,点A对应的数为______;点
对应的数为______;点
对应的数为______.(用含
的式子表示)
②若点A与点
之间的距离记为
,点
与点
之间的距离记为
,是否存在有理数
,使得代数式
的值为定值?若存在,求出
的值及该定值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/c27285711d648815c062489534b861aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/5c91d3ab-1747-42a3-bf10-893f4d74960c.png?resizew=362)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)点A以每秒2个单位长度的速度向左运动,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
②若点A与点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c113f32856af8958b7c84acc40113e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 回答下列各题.
(1)先化简,再求值:
,其中
,
.
(2)已知
,
.
①计算
;
②如果
的值与y的取值无关,求此时x的值.
(1)先化简,再求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b94686674042617f617a28dcb31737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f43cbff24a732d258091ef21bfd3af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0117b0e17dbe63ef37a59f6675a4aa99.png)
①计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a31f0e2f05bbef9aedc1b8bde981a6.png)
②如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a31f0e2f05bbef9aedc1b8bde981a6.png)
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4 . (1)数学赵老师布置了一道数学题:已知
,求整式
的值,小涵观察后提出:“已知
是多余的.”你认为小涵的说法对吗?请说明理由.
(2)已知整式
,整式
与整式
之差是
.
①求整式
;
②若
是常数,且
的值与
无关,求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ac4e28a344c68f8fa6cea2e70f974d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c7827f4ec4cd1b86f7ba1e4d310c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ac4e28a344c68f8fa6cea2e70f974d.png)
(2)已知整式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75d8e04e885dcc451e297e09d89246b8.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/a3ac5dc01996ca4ce7d7f846dfc8f83c.png)
①求整式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e769ec7d298d92206c7c5c92b2f487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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5 . 在多项式
中,不含
项,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef46943c70a228bca948d91d9e96afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
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6 . 多项式
与多项式
相减后,结果不含
项,则常数
的值为 _____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d90400bc64765631a703b78c9e2beb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a35ef142c0143280c65ff59ff9e8b5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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7 . 已知:代数式
,代数式
,代数式
.
(1)当
,
时,求代数式
的值;
(2)若代数式
的值与
的取值无关,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc84ff0456327f6940a1794a7803e6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc15c7646c1022bb9c9fc16994b28d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b71616902a786d3c3bdfc96873b2823.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若代数式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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8 . 已知代数式
,
,当x取何值时,
的值与y的取值无关.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdeb8e585fe3676ff1217fe47433671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84404c1abe7a9ecf07d868c941f7ac8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd2e0881dea2b5d4938ac48b2b1782d.png)
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9 . A、B为数轴上的两个点,点A对应的数记为a,点B对应的数记为b,且是
关于x、y的三次二项式.解答下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/8228a48a-f44f-4ff9-841d-3acf15740d35.png?resizew=403)
(1)
________,
________;
(2)若数轴上有一点C,且
,求点C对应的数;
(3)若点M、N分别从O、B出发,同时向左匀速运动,点M的速度为m个单位长度每秒,点N的速度是3个单位长度每秒,点P、Q分别为线段
、线段
的中点.设运动时间为t秒,在点M,N的运动过程中,若
的长度与t的取值无关,求m的值及
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32e3d4245fad434b65732a44b1ffa2c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/8228a48a-f44f-4ff9-841d-3acf15740d35.png?resizew=403)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)若数轴上有一点C,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3308d94691a99dd0d4aa9f28eb45dedd.png)
(3)若点M、N分别从O、B出发,同时向左匀速运动,点M的速度为m个单位长度每秒,点N的速度是3个单位长度每秒,点P、Q分别为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2138d90be06fdf900cbede5afb94d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2138d90be06fdf900cbede5afb94d3f2.png)
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10 . 已知代数式
.若
的值与
的值无关,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9db9f24664f5fbcaeadd97c5cd96f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492fde8bec43c51fc62f37af928626d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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