我们知道,函数
的图象关于坐标原点成中心对称图形的充要条件是函数
为奇函数,有同学发现可以将其推广为:函数
的图象关于点
成中心对称图形的充要条件是函数
为奇函数.
(1)请你利用这个结论求得函数
的对称中心为_________ .
(2)已知函数
与一次函数
有两个交点
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed615ff9ea5060a765c3880acf6cb34.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d0969cb7acbeaa05a101a385348a00.png)
(1)请你利用这个结论求得函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6017f4112bdd4aa7e24cac8344019f.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae3c770dcb8183855cbbd165bbc99a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c810800f20ead7f8806986d6277d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed615ff9ea5060a765c3880acf6cb34.png)
更新时间:2023-12-20 16:13:24
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【知识点】 函数对称性的应用
相似题推荐
填空题-双空题
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较难
(0.4)
解题方法
【推荐1】定义在
上的函数
满足
,且函数
的图象关于点
对称,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92682840e2a230de346562b2032f8adb.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5215a578933ba72022450a6d3a37d14.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a6442b9dec5583ff4bb93203b3f839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92146c133ba2bdbda499f5af2bdda022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92682840e2a230de346562b2032f8adb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5215a578933ba72022450a6d3a37d14.png)
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填空题-单空题
|
较难
(0.4)
【推荐2】设
是定义在
上的偶函数,
;
,若
的图象与
的图象的交点分别为
,
,……,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/017368c4fe5d82b461daa09bae240b37.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a00cda4ebde196a46cfb157653cbcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0957763a0990f21f2d24b1910cb2eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92860378096f519a8fb276d07dbfabce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7b73af3dc8b4f5cbf01551ce6f78fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9d4f56dc2eb55aaebcb5dcc125eaf72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b30470a53b058c028630ff06f74709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/017368c4fe5d82b461daa09bae240b37.png)
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