Question

Which of the following is the correct graph of the function $f\left(x\right)=\cos (3x-\frac{3\pi }{2})?$

• A.
• B.

Answer 1

The correct option is B

Given: $f\left(x\right)=\cos (3x-\frac{3\pi }{2})$

$f\left(x\right)$ can be simplified to as:
$f\left(x\right)=2\cos \{3(x-\frac{\pi }{2})\}$

Now, the graph of $\cos x$ is:

Now, shifting the graph to the right by $\pi /2$ units, we get the graph of $y=\cos (x-\frac{\pi }{2})$ as:


Now, shrinking this graph horizontally by $3$ times will give us the graph of $y=\cos 3(x-\frac{\pi }{2})$ as: