The correct option is
B ![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1419627/original_sinx.png)
In the given function
y=3cos(2x3−π)−7 , we can see that fundamental function involved is
cosx. So we will aplly some transformations to get the required graphs as follows:
Graph of fundamental function
cosx is given by
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1419631/original_sinx.png)
Now, apply stretch transformation along x-axis by
23 units as shown below to get
y=cos(2x3) as shown below
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1419634/original_sinx.png)
Further, apply the horizontal shift by
3π2 units to get
y=cos(2x3−π) as
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1419638/original_sinx.png)
Here we need to apply vertical stretch by 3 units to obtain graph of
y=3cos(2x3−π) as
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1419639/original_sinx.png)
finally apply the vertical shift of 7 units in above to get
y=3cos(2x3−π)−7
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1419641/original_sinx.png)
Whihc is required graph of
y=3cos(2x3−π)−7 and correct match is option (d).