1 . 对于两条平行直线
、
(
在
下方)和图象
有如下操作:将图象
在直线
下方的部分沿直线
翻折,其余部分保持不变,得到图象
;将图象
在直线
上方的部分沿直线
翻折,其余部分保持不变,得到图象
:再将图
在直线下方的部分沿直线
翻折,其余部分保持不变,得到图象
;再将图象
在直线
上方的部分沿直线
翻折,其余部分保持不变,得到图象
;以此类推…;直到图象
上所有点均在
、
之间(含
、
上)操作停止,此时称图象
为图象
关于直线
、
的“衍生图形”,线段
关于直线
、
的“衍生图形”为折线段
.
(1)直线型
平面直角坐标系中,设直线
,直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7712260b9136c187e571f2e52b07ff.png)
①令图象
为
的函数图象,则图象
的解析式为
②令图像
为
的函数图象,请你画出
和
的图象
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/8bf8f6d6-91ee-4f7e-acda-5423f6753233.png?resizew=380)
③若函数
的图象与图象
有且仅有一个交点,且交点在
轴的左侧,那么
的取值范围是_______.
④请你观察图象
并描述其单调性,直接写出结果_______.
⑤请你观察图象
并判断其奇偶性,直接写出结果_______.
⑥图象
所对应函数的零点为_______.
⑦任取图象
中横坐标
的点,那么在这个变化范围中所能取到的最高点的坐标为(_______,_______),最低点坐标为(_______,_______).
⑧若直线
与图象
有2个不同的交点,则
的取值范围是_______.
⑨根据函数图象,请你写出图象
的解析式_______.
(2)曲线型
若图象
为函数
的图象,
平面直角坐标系中,设直线
,直线
,
则我们可以很容易得到
所对应的解析式为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/70a2b9bc-043f-460f-bbc7-52b4eb8ed5f5.png?resizew=367)
①请画出
的图象,记
所对应的函数解析式为
.
②函数
的单调增区间为_______,单调减区间为_______.
③当
时候,函数
的最大值为_______,最小值为_______.
④若方程
有四个不同的实数根,则
的取值范围为_______.
(3)封闭图形型
平面直角坐标系中,设直线
,直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25081197c462bd7f03cc67c35c85593d.png)
设图象
为四边形
,其顶点坐标分别为
,
,
,
,四边形
关于直线
、
的“衍生图形”为
.
①
的周长为_______.
②若直线
平分
的周长,则
_______.
③将
沿右上方
方向平移
个单位,则平移过程中
所扫过的面积为_______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fda993d38532293724009685288b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fda993d38532293724009685288b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a12119eba9da5c32568de5832ff04c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a12119eba9da5c32568de5832ff04c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16365b04bc8aa6787782e0aef019342d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47341a477c35b3044c5519ea8404494d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47341a477c35b3044c5519ea8404494d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc6caaae3d88eaf009ae496d2788134.png)
(1)直线型
平面直角坐标系中,设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ba5c616b58eb33dbd5a2690f003f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7712260b9136c187e571f2e52b07ff.png)
①令图象
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
②令图像
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fda993d38532293724009685288b72.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/8bf8f6d6-91ee-4f7e-acda-5423f6753233.png?resizew=380)
③若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76ba1c1cef5f0e6efdca5e436122412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
④请你观察图象
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fda993d38532293724009685288b72.png)
⑤请你观察图象
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fda993d38532293724009685288b72.png)
⑥图象
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fda993d38532293724009685288b72.png)
⑦任取图象
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fda993d38532293724009685288b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56628de19272fbf3803dfa8d617ba779.png)
⑧若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50683751e9dcd7b55555b53785f61a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fda993d38532293724009685288b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
⑨根据函数图象,请你写出图象
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fda993d38532293724009685288b72.png)
(2)曲线型
若图象
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c962d7485825381801f1ebf56a37ec.png)
平面直角坐标系中,设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ba5c616b58eb33dbd5a2690f003f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7712260b9136c187e571f2e52b07ff.png)
则我们可以很容易得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cffe34fde5a4f8ed96b1394acad8b4c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/70a2b9bc-043f-460f-bbc7-52b4eb8ed5f5.png?resizew=367)
①请画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8160ade472b89421f8009fd0cd3926a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
④若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99d3ec153c1dd00d0185bc14b4f56b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)封闭图形型
平面直角坐标系中,设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ea6e5fa7672c43a45ebb4c3757370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25081197c462bd7f03cc67c35c85593d.png)
设图象
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b978a095d4bac4da3a807575d9b35e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847fea08d7cb36942bd5028b2cb7707e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae4febd9d6318cb2cfd23ac9dd2922e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2c5dbea60dd70fbbeb390c094859cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b978a095d4bac4da3a807575d9b35e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47341a477c35b3044c5519ea8404494d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47341a477c35b3044c5519ea8404494d.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a806c58799f9bac6c601aee7aad5bb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47341a477c35b3044c5519ea8404494d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
③将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47341a477c35b3044c5519ea8404494d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47341a477c35b3044c5519ea8404494d.png)
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