Question

The graph of y=sin(x-3x/2) is the graph of the y=sin(x) shifted in which direction?

Answer 1

3x/2 units to the right, so b).
It's not c) or d), because the -3x/2 is within the sin, rather than outside like y=sin(x)-3x/2
If it were shifted to the left, the equation would be y=sin(x+3x/2)

Answer 2

Answer:

b. $\frac{3\pi}{2}$ to the right.

Step-by-step explanation:

We are asked to find the translation applied on graph of $y=\text{sin}(x)$ to get $y=\text{sin}(x-\frac{3\pi}{2})$

Let us recall the translation rules.

$f(x+a)=\text{Graph shifted to left by a units}$

$f(x-a)=\text{Graph shifted to right by a units}$

Upon looking at our given transformation we can see that graph of $y=\text{sin}(x)$ is shifted to right by $\frac{3\pi}{2}$ units to get $y=\text{sin}(x-\frac{3\pi}{2})$.

Therefore, option 'b' is the correct choice.