1 . 如图,指数函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036710b9ce94be1dc185f4608efdadb1.png)
与直线
分别交于点A,B,C,若A,B,C的横坐标分别为
,满足
,则![](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/036710b9ce94be1dc185f4608efdadb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bc968aa51d4f8addb7e61b9fd73a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5a4e42606d7d5e8e7164b380b7fe27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128f8ee81d3c26d069c69719dd41bdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65f7eb3681f8fb242c194ba16c0d3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/7d9364ce-b604-4730-8a01-0ed4ed6f6db6.png?resizew=163)
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2 . 给定函数
,若在其定义域内存在
使得
,则称
为“
函数”,
为该函数的一个“
点”.设函数
,若
是
的一个“
点”,则实数
的值为________ .若
为“
函数”,则实数
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7325d2b5f25f64ada66dd8d191fe8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744b07c137166e10db0b54001cb93a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93defceb5d09d596bfc173e5728cfa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0639fc72ab32053765a65a2c38852927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
3 . 已知函数
,用
表示
中的较小者,记为
,则函数
的最大值为______ ;若
,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584f5b60deca105f8e03d1719d1662df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0ed188d083966baaae94e6b86064f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241541a56cadaf957535d9a432a1e0e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e62973b17bd7d238ee53702ff78dfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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4 . 设
,函数
,当
时,
的值域是______ ;若
恰有一个零点,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f306d2b261f4c39a9fc0858d96e647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93955c5a47d255c0990f336a5fc2779b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ea0e903fbb4c8ce04133b9969578c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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5 . 已知函数
,当
时,不等式
的解集是______ ,若
恰有2个零点,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68dfcd9c934fc39cff91f2ee0652599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
6 . 已知
,其中
.若
,则
的取值范围是__________ ;若
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a4e995f5e101850da77a3623fa12a47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae684ce1627b48e99aedff6808d01b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e51572776a92112a0bc85342807c5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
7 . 已知
.若
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ ;若
的图像关于原点对称,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffaae0b3447320096ee665492bdf04b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be718751a03ecb04f75e25e917d71a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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解题方法
8 . 若闭区间
满足:①函数
在
上单调;②函数
在
上的值域为
,
,则称区间
为函数
的
次方膨胀区间. 函数
的2次方膨胀区间为_____________ ;若函数
存在4次方膨胀区间,则
的取值范围是_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91393ddcf411f513b77caad29a31cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6724c68c4206bd95683998d800f7f676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a993d222157197c263ae4a8255228a69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c4821d3e69fbb6a1f8d0afe0d725f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
9 . 已知函数
的定义域为
,满足
,
的图象关于直线
对称,且
,则
______ ;
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e21b60b8b5fffe78a4fe3aed643ed925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e356a6e54a669fda721085096c8416db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0632bc67a48ee16de53fe7e19ec3328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a7798f78f349848294ebdbc001c9cb.png)
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10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
函数
有______ 个零点;若方程
有三个不相等的实数根,则k的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6240529d96b6b1d246df53aeaacf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d64ef97b7ba8001ae416b5e8c3f42c.png)
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