已知有理数a,b,c在数轴上的位置如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/17/130f9123-65bf-43db-ae25-f3140289d9f9.png?resizew=258)
(1)用符号“<,>,=”填空:
0,
0;
(2)化简:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/17/130f9123-65bf-43db-ae25-f3140289d9f9.png?resizew=258)
(1)用符号“<,>,=”填空:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7fa17a39f52e09981729af4439ca535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcd4220736032d542634dfc80c08ff4.png)
更新时间:2023-11-07 13:18:23
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【推荐1】已知,数a、b、c在数轴上的位置如图:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/930fce35-9d32-4118-a4bd-552de1e44d45.png?resizew=266)
(1)判断正负,用“>”或“<”连接:
0,
0,
0;
(2)化简:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/930fce35-9d32-4118-a4bd-552de1e44d45.png?resizew=266)
(1)判断正负,用“>”或“<”连接:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db8d3facff8f90f28a936fc5b3ab878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e4d93d6487777af953af02c1be6f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf6dfee4181b3df1eb44e754df4861a.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c505e768e9f5bdd3c48d51ce2e2d79a3.png)
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【推荐2】有理数
、
、
在数轴上的位置如图:
(1)
______0;
______0;
(2)化简
.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531fead92fcb98f6fe36d84c7820804e.png)
![](https://img.xkw.com/dksih/QBM/2021/11/29/2861835627257856/2863265524703232/STEM/f21660b1-d4ee-4d84-93e9-dbfd32cc4530.png?resizew=343)
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【推荐1】有理数
,
,
在数轴上的位置如图所示,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/62183cf9-5882-400b-a3e4-c28aaaac8f12.png?resizew=302)
(1)填空:
;
.(用“
”或“
”或“
”填空)
(2)化简代数式:
.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850f6874ea501c6021573701b0294dcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/62183cf9-5882-400b-a3e4-c28aaaac8f12.png?resizew=302)
(1)填空:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ad90e7668dbe9b76f98f8176313501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d15c3676d98a5ebff31cd27dd481a3b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
(2)化简代数式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e91b1578d02e343a87028e55166e3c.png)
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【推荐2】在解决数学问题的过程中,我们常用到“分类讨论”的数学思想,下面是运用分类讨论的数学思想解决问题的过程,请仔细阅读,并解答问题.
【提出问题】三个有理数a,b,c满足
,求
的值.
【解决问题】解:由题意,得a,b,c三个有理数都为正数或其中一个为正数,另两个为负数.
①a,b,c都是正数,即
,
,
时,则
;
②当a,b,c中有一个为正数,另两个为负数时,不妨设
,
,
,则
.
综上所述,
值为3或
.
【探究拓展】请根据上面的解题思路解答下面的问题:
(1)已知a,b是不为0的有理数,当
时,则
的值是______;
(2)已知a,b,c是有理数,当
时,求
的值;
(3)
,且
,则
的值.
【提出问题】三个有理数a,b,c满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c21bd0bd90a89b7ff5ac0eacf612a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce563ace106dd7eb696cf3a293d83d9c.png)
【解决问题】解:由题意,得a,b,c三个有理数都为正数或其中一个为正数,另两个为负数.
①a,b,c都是正数,即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c9fc938195e1ce9d973934cd1f81f7e.png)
②当a,b,c中有一个为正数,另两个为负数时,不妨设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a915c1a8a9304aeb307d130faaeb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75807858b7804a1ad2039c41f323a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888cad31ccc4e58bfe79d6d0df0042a.png)
综上所述,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce563ace106dd7eb696cf3a293d83d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
【探究拓展】请根据上面的解题思路解答下面的问题:
(1)已知a,b是不为0的有理数,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35893617de39cae7294e51b764d0450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524a8f0aec8d5e9ef76071eaff5ead6a.png)
(2)已知a,b,c是有理数,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77694c11ba40ec5c2fc4f6a05e31a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fefef55f006747897696fe614cd877a7.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e96f2368d04db6d0e05de46e97e29f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01ea3943a98c8c30d46555e48ff7f2f.png)
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解答题-作图题
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【推荐3】在学习一次函数时,我们学习了列表、描点、连接画函数图像,并结合函数图像研究函数的性质.同时,在初一的时候我们学习了绝对值的意义:
.请你完成下列问题.
(1)【尝试】①当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7555809362059827c8082a96af196c17.png)
②当
时,
______.
③当
时,
______.
(2)【探索】探究函数
的图像与性质.
①请完成以下列表:
②请根据①中的表格,在给出的平面直角坐标系中画出
的图像.
(3)【拓展应用】若关于x的方程
有且只有一个正的解和一个负的解,则m的取值范围是______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43457b9ce854e7c22fa7b0ce7c5178f.png)
(1)【尝试】①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7555809362059827c8082a96af196c17.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200849ce71f53c0321506e27de437b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31a677f25f0b55ee178e4711f7271da.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31a677f25f0b55ee178e4711f7271da.png)
(2)【探索】探究函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb58192b86746291c5eff88e77c79d7.png)
①请完成以下列表:
x | …… | ﹣1 | 0 | 1 | 2 | 3 | 4 | 5 | …… |
y | …… | 3 | …… |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb58192b86746291c5eff88e77c79d7.png)
(3)【拓展应用】若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9daba949cc8f7afb6a1bc91186265d2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/539d34ee-0e38-4815-8d55-53de05f09df1.png?resizew=290)
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