在数学学习中,及时对知识进行归纳和整理是完善知识结构的重要方法.善于学习的小明在学习了二元一次方程
组
、一元一次不等式和一次函数后,把相关知识归纳整理如下:
(1)请根据以上方框中的内容在下面数字序号后写出相应的结论:
①______;②______;③______;④______.
(2)若点
,
,
的坐标分别为
、
、
,则方程
的解为______;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/9/a159168e-a252-4adf-8b1f-28cc1d04bffd.png?resizew=166)
不等式
的解集为______;
不等式
的解集为______;
不等式组
的解集为______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
一次函数与方程的关系: (1)一次函数的解析式就是一个二元一次方程; (2)点 ![]() (3)点 ![]() ![]() ![]() ![]() 一次函数与不等式的关系: (1)函数 ![]() ![]() ![]() ![]() (2)函数 ![]() ![]() ![]() ![]() |
①______;②______;③______;④______.
(2)若点
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4db5cd35afd7da6256efa25c61c7341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f104804c2174b5b6f62f70ff8e47a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7c53ed30f6290801c54f6db61dd4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c2113ce7bd9aec6d6144e3705d7a0d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/9/a159168e-a252-4adf-8b1f-28cc1d04bffd.png?resizew=166)
不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc839267f395e64b1932874607138418.png)
不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc62e5d136cf095ee2c55a393b322822.png)
不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26021c5a400d730718b963c598c343af.png)
更新时间:2022-08-06 20:46:40
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相似题推荐
解答题-作图题
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【推荐1】一次函数
的图像经过点
和
.
(1)求这个一次函数的表达式;
(2)画出该函数的图像;
(3)结合图像回答:当
时,x的取值范围是______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5d501afbd7542f2f724b658edf39af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483dd3a65702ed0cd7df766300d03b3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/3/603edd39-d5e4-4bdf-9f23-081a2fe7ba78.png?resizew=241)
(1)求这个一次函数的表达式;
(2)画出该函数的图像;
(3)结合图像回答:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57458464618fcf619375a93d3c66d69.png)
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解答题-证明题
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【推荐2】设一次函数
(k,b是常数,且
).
(1)若一次函数
和
的图象交于x轴同一点,求
的值.
(2)若
,
,点
和
在一次函数y的图象上,且
,求
的取值范围.
(3)若
,点
(
)在该一次函数上,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
(1)若一次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f25ca6ba3b1abc3443093f32360d1b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02f266bd253738e315e84231235f0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc0b93c37d337d5aabfc46396beb7a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59580656f890f5340f7c10531e15ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c394559f81cc114b23556ddab2479b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec8c9d200bb6b98777c302a476938937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
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解答题-问答题
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【推荐1】一次函数
和
的图象如图所示,且
,
.
的解集是______;
(2)若不等式
的解集是
.
①点
的坐标为______.
②
的值为_______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed06ccefffc165f9c77250cd28301d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14f5df1d01e5740825285cceaf99ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c84818cfbd9a885081cb4e3294eabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dd31773f55719ebd91ed3389d0de68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2873942b9f3141213ecd93f42aa270d9.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8357b27a2b3d2d76de1b31099285cbbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解答题-问答题
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【推荐2】在平面直角坐标系
中,直线
与直线
平行,且经过点
.
(1)求直线
的解析式;
(2)已知直线
,过点
作
轴的垂线,与直线
交于点
,与直线
交于点
.
结合图象回答:
①若
,当点
在点
的上方时,直接写出
的取值范围;
②若对任意的
,都有点
在点
的上方,直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51a109f8365293a6d3c149047d352f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455fc890c91336af8159f97db432eccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5924a9517d09ed07ac44b442c3e3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
结合图象回答:
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
②若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153fb853cd99beec9e600a4eaf73fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://img.xkw.com/dksih/QBM/2021/9/15/2808736061186048/2820720783933440/STEM/d4ac3a89e6174066bde4cdb7e696d8b5.png?resizew=173)
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解答题-作图题
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名校
【推荐3】学习一次函数时,我们通过列表、描点、连线画出一次函数图象,并结合函数图象研究函数性质.小米结合学习一次函数的经验,对函数
的图象和性质进行了研究,下面是小米的探讨过程,请补充完整:
(1)列表:
表格中m=_______;n= __________;
(2)描点、连线;
①在图中画出该函数图象;
②结合图象,写出该函数的一条性质: ;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/7/ec3f5202-7bcc-4af6-a3f7-39363fdc2eb4.png?resizew=179)
(3)过点(0,a)作直线l∥x轴,结合所画的函数图象,若直线l与函数
图象有两个交点,则a的取值范围是________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6704a7416b541c47cf794ce7e5644484.png)
(1)列表:
x | … | -2 | -1 | 0 | 1 | 2 | 3 | … |
y | … | m | 1 | 2 | 3 | 2 | n | … |
(2)描点、连线;
①在图中画出该函数图象;
②结合图象,写出该函数的一条性质: ;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/7/ec3f5202-7bcc-4af6-a3f7-39363fdc2eb4.png?resizew=179)
(3)过点(0,a)作直线l∥x轴,结合所画的函数图象,若直线l与函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6704a7416b541c47cf794ce7e5644484.png)
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