1 . 已知函数
的部分图象如图所示.
的解析式及其单调递增区间;
(2)将函数
的图象上所有的点向右平移
个单位,再将所得图象上每一个点的横坐标变为原来的2倍(纵坐标不变),得到函数
的图象.若方程
在
上有三个不相等的实数根
,
求①求m的取值范围.
②求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb2b2fdc4e57e2d2de7115758518622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a09da1efd0f599dd4682f2284822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a604fadcbf8568cbd8dacddd68443e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f2c9ba604e34100159eb10cccd2b04.png)
求①求m的取值范围.
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a8516b1db6979a28b07fd841c7f06b.png)
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解题方法
2 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc7e499a99496563ba14bea539e9ff1.png)
A.![]() ![]() |
B.![]() ![]() |
C.若方程![]() ![]() ![]() ![]() |
D.若方程![]() ![]() ![]() ![]() ![]() |
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3 . 初中学过多项式的基本运算法则,其实多项式与方程的根也有密切关联.对一组变量
,幂和对称多项式
,且
;初等对称多项式
表示在
中选出
个变量进行相乘再相加,且
.例如:对
.已知三次函数
有3个零点
,且
.记
,
.
(1)证明:
;
(2)(i)证明:
;
(ii)证明:
,且
;
(3)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b85069b184b032808ce05636373b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d15873316d0c17fbcbbe376834e5697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63239fb9313458d7f86b64d2860beba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba0d57c2c8fcc1cef3a02b67d4193b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca373f163399198a6beb169fe6df5262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef4ab1ca44d62d6451f85e41258abe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5f85f6501033a93c8be7363d59c8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489340c9a2d70c00bae13b7018cad448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93e7bb2538cf1dcb50722aa9cf0550c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38c64a6143b210aa315e0b6bfaccf94.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e856070d58b6aefce7e914426d7f95c.png)
(2)(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549ef2a5b6592308c2da9233aca63e77.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6429dd74013b8984de8dcaac9c862957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52121b304f70afcb2dfb3d4a614f7224.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d177a7489e327bff83e61ac1eeaaf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5235bf88c507cd6178e94914133d04.png)
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4 . 已知函数
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea28d727a773f3265bc66aff642713a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039f9392112593405d4c0f1bea7d31f3.png)
A.若![]() ![]() |
B.当![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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5 . 对于定义域为
的函数
,若
,使得
,其中
,则称
为“可移
相反数函数”,
是函数
的“可移
相反数点”.已知
,
.
(1)若
是函数
的“可移2相反数点”,求
;
(2)若
,且
是函数
的“可移4相反数点”,求函数
的单调区间;
(3)设
若函数
在
上恰有2个“可移1相反数点”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c42ef103bbb40a9c414ba273a16fa32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54739d72b5c319dcb4a6bc632256e813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6263576e5c3f2324a8dac311476bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670f35aac7f9bd8acf6fc5cd4e119b59.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6c0bbfde440305a1de1e939ac78082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01ff53404ba146b39bd9e12dd68afbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 不经过第四象限的直线
与函数
的图象从左往右依次交于三个不同的点
,
,
,且
,
,
成等差数列,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4c6592bbbee1498da630bd431299fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132668fc41c8266ba917dc5b4995c6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0a4d02005ed2c048b59856ad98c030.png)
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7 . 设函数
在
上有且仅有1个极值点和1个零点,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9429ade94a205c5e354596df5bc1f71c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579b9c272915b330e5fc8766885f99e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbb2b6c196e5e15f85900eb4325513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 已知函数
,若关于
的方程
有4个不同的实根
、
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c407c501c66aa304839fe61ff531d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2961ff859ef31f3a71c69841dc64176f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f176de330ed3f93fee6f5a398de57c3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知函数
,若方程
有三个不相等的实数解,则实数a的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c5b5988876dc6e10cf9eca3fc33cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1542ce83034144ffcfa273d7481bd7de.png)
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10 . 已知函数
(
)在
有且仅有三个零点,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79417be37bf2b1cebd244e97e96bc2a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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