1 . 如图,对数函数
图象上的点A与x轴上的点
,C构成以BC为斜边的等腰直角三角形,若
右侧的相似三角形
的顶点E在函数
上,顶点C,D在x轴上,且两三角形的相似比为2,则该对数函数的解析式为______ .,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c82cafa7ea341764fdccd42b2680200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/05791cd0-774c-44fd-accc-eae8a8e367c3.png?resizew=163)
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23-24高一上·江苏·课后作业
2 . (1)对对数函数
(
),当
越来越小时,其图象与_____ 的负半轴越来越靠近;对对数函数
(
),当
越来越小时,其图象与_____ 的正半轴越来越靠近.
(2)对于对数函数
的图象,在第一象限内,当
时,底数越大,图象越_____ ;当
时,底数越小,图象越_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)对于对数函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ad83d265323cf71db50956e0eb39ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
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名校
3 . 在下列四个函数中任选两个相加可以得到6个新的函数:
①
②
③
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
其中有无数个零点的所有函数为_____________ (写出完整的函数解析式)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
其中有无数个零点的所有函数为
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4 . 设
且
,若在平面直角坐标系xOy中,函数
与
的图像于直线l对称,则l与这两个函数图像的公共点的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bbb80619d6e1312fba9cd3a02c8f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947a492a80e26798f9570e190d0207a2.png)
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22-23高一上·北京·期末
解题方法
5 . 已知函数
,
,
(
且
),给出下列四个结论:
①当
时,对
,函数
的图象恒在函数
的图象上方;
②当
时,函数
与
的图象有两个交点;
③
,当
时,恒有
;
④
,方程
,
,
都有解.
其中正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d76ee3b131ecd6aa1aacf7fb7b3eb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84518e68c9e73dee93a8a3cafce4d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ca4dec0b8e14b9acb6463758488893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81b4aac721bcd4a49593b48a28a8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c12e17e20663e384f0e193b4435c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119c13383d9a3838ad3b6342ce720a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36d24aa0af9ae8c0ab895b651e22aea.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f2a980e8f3ef76cd4558c53a8e6d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade50791b5cb67652b1f0405707a90cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacf3f0e1424b7ed50d58a4c7ec9b378.png)
其中正确结论的序号是
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21-22高一·全国·课后作业
6 . 判断正误
(1)对数函数的定义域为R.( )
(2)
与
都不是对数函数.( )
(3)对数函数的图象一定在y轴右侧.( )
(1)对数函数的定义域为R.
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e3b66275361ad50fb8728f0bc28584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf605ad3d204601efb0421d693d3708.png)
(3)对数函数的图象一定在y轴右侧.
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