Question

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

a) 3x/2 units to the left

b)3x/2 units to the right

c)3x/2 units up

d)3x/2 units down

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

b.
`(3\pi)/(2)` to the right.

Explanation:

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

Therefore, option 'b' is the correct choice.