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

A3x/2 units to the left

b)3x/2 units to the right


c)3x/2 units up


d)3x/2 units down

Verified Answer :

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:

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.

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