解题方法
1 . 函数
的值域为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fa3c37cabebaae55e24e9f63b881c6.png)
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解题方法
2 . 有四个幂函数:①
,②
;③
;④
.某同学研究了这几个函数,并给出函数的三个性质:(1)偶函数;(2)值域是
;(3)在
上是增函数.如果给出的三个性质中,有两个正确,一个错误,则满足条件的函数是______ (填序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8756b76b2fb3289cb0f5a38623d5e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4546e5f3a8fdff3206eeb2950ebd44a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af07d272da54872ad5a5d2c8181760af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7192d87d0fa400d5d7dba57924bbbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d609abb6046a5846e8e436d3196461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
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名校
解题方法
3 . 写出一个同时具有下列三个性质的一个幂函数:______ .
(1)偶函数;(2)值域是
;(3)在
上是增函数.
(1)偶函数;(2)值域是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885be9fdb5be34b02ac22beb050d4975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
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解题方法
4 . 已知函数
(
),写出一个同时满足下列性质①②的
的值:______ .
①当
时,
;②
在
上单调递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f98703a94efdf092738b9b9cc431b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17cda8268bfbe1ba1a6eb4ac797b536b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b12f2ff24c52fded1dfd0f0b6940a2.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/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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名校
解题方法
5 . 若
,
,使得
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4598cc5d24e6af27e60e0857b1f4489a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab58b21c5de3a91db6c001d410b2eff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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解题方法
6 . 已知
,则使函数
的值域为R,且为奇函数的所有α的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffd8eb49297e87a894730dc4f781da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd3f86cd7afe812f3d8e131bee1e315.png)
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7 . (1)函数
的定义域是__________ ,值域是__________ ;
(2)函数
的定义域是__________ ,值域是__________ ;
(3)函数
的定义域是__________ ,值域是__________ ;
(4)函数
的定义域是__________ ,值域是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796e9d1ce6db5a9ae006b16a5511707d.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b026fe3e532108d7a415f5c4f0f1ce12.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884e534313d810d5fc36b95f9fcaa08.png)
(4)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2037b5cf0764ca2446ec2fe60b7ba04a.png)
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2023高三·全国·专题练习
解题方法
8 . 已知集合
,
,若
,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921b1f3c0fea4b2f41580346d4dd9a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658a64d1a60fddb4b06d0efb5aa216ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2333f966f6ec29f0661f93d99b055cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . 直线
:
与
,
轴的交点分别是
,
,
与函数
,
的图像的交点分别为
,
,若
,
是线段
的三等分点,则
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a443d72bb06ba9714ed82f84b0ed186d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da668452bf94a7df60422815ae3b3d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a222f26066420db184ee783541d80b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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10 . 已知函数
.直接在下表中写出其定义域、值域,指出其在定义域上的单调性、奇偶性,并判断其是否存在零点,若存在零点请写出具体零点(不需要写过程,将答案填在表格中).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b87e78256e9afeb56ef82106e9d895.png)
定义域 | |
值域 | |
单调性 | |
奇偶性 | |
零点 |
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