Question

Correct graph of the function $y=3\cos (\frac{2x}{3}-\pi )-7$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

In the given function $y=3\cos (\frac{2x}{3}-\pi )-7$ , we can see that fundamental function involved is $\cos x$. So we will aplly some transformations to get the required graphs as follows:

Graph of fundamental function $\cos x$ is given by
Now, apply stretch transformation along x-axis by $\frac{2}{3}$ units as shown below to get $y=\cos \left(\frac{2x}{3}\right)$ as shown below
Further, apply the horizontal shift by $\frac{3\pi }{2}$ units to get $y=\cos (\frac{2x}{3}-\pi )$ as
Here we need to apply vertical stretch by 3 units to obtain graph of $y=3\cos (\frac{2x}{3}-\pi )$ as
finally apply the vertical shift of 7 units in above to get $y=3\cos (\frac{2x}{3}-\pi )-7$


Whihc is required graph of $y=3\cos (\frac{2x}{3}-\pi )-7$ and correct match is option (d).