解题方法
1 . 定义:若将函数
的图象平移可以得到函数
的图象,则称函数
,
互为“平行函数”.已知
,
互为“平行函数”.
(1)判断并证明函数
的单调性;
(2)求实数a的值;
(3)求由函数
的图象、函数
的图象及y轴围成的封闭图形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c34d64a7bea0629324b9105d94556ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b8100c54a46bb7f8ba778307d7b03d.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求实数a的值;
(3)求由函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a5ff72ba4e9d01ecf0c0fe07a48058.png)
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名校
解题方法
2 . 已知函数
是定义在R上的偶函数,且当
时,
,现已画出函数
在y轴左侧的图象(如图所示),请根据图象解答下列问题.
(1)作出
时,函数
的图象,并写出函数
的增区间;
(2)用定义法证明函数
在
上单调递减.
(3)若函数
在区间
上具有单调性,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5397ee1eb6d157f6ec1e7a878f8d16e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/d92e384f-155f-419a-979f-8b1ec932f027.png?resizew=222)
(1)作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用定义法证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c82644f77c5455ceb7f94950e94273.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55503c093ffb545056ba2a313f21b25e.png)
您最近一年使用:0次
2023-11-09更新
|
313次组卷
|
2卷引用:江西省上饶市上饶中学2023-2024学年高一上学期期中考试数学试题
解题方法
3 . 已知函数
.
(1)画出
的图象;
(2)若函数
的最小值为m,x,y,
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd95b79f0d36b83f348ae730ba3c4a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/7/d3d9876a-a4a1-4b67-a6af-dfcaf7d4245c.png?resizew=175)
(1)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc7e635200cb19c4730160bb359f5f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9840dfad60acd1cb4198270481849b0.png)
您最近一年使用:0次
2023-08-04更新
|
82次组卷
|
2卷引用:江西省赣州市兴国县2023届高三高考考前最后一卷(全国乙卷)数学(理)试题
4 . 设
,
,且a、b为函数
的极值点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650b262681fdf608130ab36553b24009.png)
(1)判断函数
在区间
上的单调性,并证明你的结论;
(2)若曲线
在
处的切线斜率为
,且方程
有两个不等的实根,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf717b54f199a2fcb28e988fc2da8f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f139fc1ad6e0cb114f1c6e2be1dfa995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650b262681fdf608130ab36553b24009.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd2a15b848dbede398dac79c22a017b.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e09f43349742cd3e95d75ffa7f17fbd4.png)
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