2022年1.5函数y=Asin的图象 .pdf

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1、yxsin()31.5 函数 y=Asin（x+）的图象教学目的：1、理解振幅变换和周期变换和平移变换;会用图象变换的方法画yAsin（x）的图象；2、会用“五点法”画 yAsin（x）的图象；3、会求一些函数的振幅、周期、最值等；4、渗透分类讨论的数学思想，提高分析和解决问题的能力。教学重点、难点重点：用图象变换的方法画yAsin（x）的图象。难点：理解振幅变换和周期变换和平移变换。教学过程：一、复习引入：1正弦曲线-11yx-6-565-4-3-2-0432f x =sin x2.余弦曲线-11yx-6-565-4-3-2-0432f x =cos x3.五点法做图二、讲授新课：1、函数图

2、象的左右平移变换如在同一坐标系下，作出函数和的简图，并指出它们与yxsin图象之间的关系。的周期为2，我们来作这个函数在长度为一个周期的解析：函数闭区间上的简图。设xZ3，那么sin()sinxZ3，xZ3当 Z 取 0、2322、时，x 取36237653、。所对应的五点是函数yxsin()3，x353，图象上起关键作用的点。列表：x 36237653x30 2322sin()x30 1 0 1 0 yxsin()4yxsin()3类似地，对于函数yxsin()4，可列出下表：x 434547494x40 2322sin()x40 1 0 1 0 描点作图（如下）利用这类函数的周期性，可把所

3、得到的简图向左、右扩展，得出yxsin()3，xR及yxsin()4，xR的简图（图略）。由图可以看出，yxsin()3的图象可以看作是把yxsin的图象上所有的点向左平行移动3个单位而得到的，yxsin()4的图象可以看作是把yxsin的图象上所有的点向右平行移动4个单位得到的。注意：一般地，函数yxsin()()0的图象，可以看作是把yxsin的图象上所有的点向左（当0时）或向右（当0时）平行移动|个单位而得到的。2、函数图象的纵向伸缩变换如 在 同 一 坐 标 系 中作 出yx2sin及yx12sin的 简 图，并 指 出 它 们 的 图 象 与yxsin的关系。文档编码:CK8R9M2

4、Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M

5、1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S

6、4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9

7、M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P

8、7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B

9、5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8

10、R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9解析：函数yx2sin及yx12sin的周期T2，我们先来作x02，时函数的简图。列表：x 0 2322sinx 0 1 0 1 0 2sinx 0 2 0 2 0 12sinx0 120 120 描点作图，如图：利 用 这 类 函 数 的 周 期 性，我 们 可 以 把 上 图 的 简

11、 图 向 左、向 右 扩 展，得 到yxxR2sin，及yxxR12sin，的简图（图略）。从上图可以看出，对于同一个x 值，yx2sin的图象上点的纵坐标等于yxsin的图象上点的纵坐标的两倍（横坐标不变），从而yxxR2sin，的值域为 2，2，最大值为 2，最小值为 2。类似地，yx12sin的图象，可以看作是把yxsin的图象上所有点的纵坐标缩短到原来的12倍（横坐标不变）而得到的，从而yxxR12sin，的值域是1212，最大值为12，最小值为12。注意：对于函数yAxsin（A0 且 A1）的图象，可以看作是把yxsin的图象上所有点的纵坐标伸长（当A1 时）或缩短（当0A0，0，

12、x)0，）表示一个振动量时，A 就表示这个量振动时离开平衡位置的最大距离，通常把它叫做这个振动的振幅；往复振动一次所需要的时间T2，它叫做振动的周期；单位时间内往复振动的次数fT12，它叫做振动的频率；x叫做相位，叫做初相（即当x0 时的相位）。三、典型例题文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK

13、8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2

14、B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5

15、O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:

16、CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 H

17、K2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 Z

18、U5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9例 1

19、.用两种方法将函数yxsin的图象变换为函数yxsin()23的图象。分析 1：xxxx22623()解法 1：yxsin横坐标缩短到原来的纵坐标不变12yxsin26向左平移个单位yxxsin()sin()2623分析 2：xxx323解法 2：yxsin向左平移个单位3yxsin()312横坐标缩短到原来的纵坐标不变yxsin()23注意：在解法 1 中，先伸缩，后平移；在解法2 中，先平移，后伸缩，表面上看来，两种变换方法中的平移是不同的（即6和3），但由于平移时平移的对象已有所变化，所以得到的结果是一致的。例 2.用五点法作出函数yx223sin()的图象，并指出函数的单调区间。解：（

20、1）列表列表时23x取值为 0、2、32、2，再求出相应的x 值和 y 值。x 61237125623x0 2322y 0 2 0-2 0（2）描点（3）用平滑的曲线顺次连结各点所得图象如图所示：利 用 这 类 函 数 的 周 期 性，我 们 可 以 把 上 面 所 得 到 的 简 图 向 左、右 扩 展，得 到yx223sin()，xR的简图（图略）。文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M

21、9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2

22、Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M

23、1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S

24、4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9

25、M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P

26、7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B

27、5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9可见在一个周期内，函数在12712，上递减，又因函数的周期为，所以函数的递减区间为kkkZ12712，()。同理，增区间为()kkkZ51212，。例 3.如图是函数yAxsin()的图象，确定A、的值。解：显然 A2 T566()222Tyx22sin()解法 1：由图知当x6时，y0 故有2260 x()，3所求函数解析式为yx223sin()解法 2：由图象可知将yx22sin的图象向左移6即得yx226sin()，即yx223sin()3四、课堂练习：课本 62 页练习第1、2、3、4、题五、课

28、堂小结略六、作业课本第 65 页习题 A组第 1、3 题 B组第 2、3 题文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1

29、 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10

30、 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文

31、档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1

32、S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O

33、10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9文档编码:CK8R9M2Z1S1 HK2B3P7M1O10 ZU5O6B5S4M9