Answer: [tex]\bold{D)\quad y = 2sin(3x)}[/tex]
Step-by-step explanation:
[tex]\text{The standard form of a sine equation is: y=A sin(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]
In the given graph,
- A (amplitude) = 2
- P (period) = [tex]\dfrac{2\pi}{3}[/tex] --> B = 3
- Phase Shift [tex]\bigg(\dfrac{C}{B}\bigg)[/tex] = 0 --> C = 0
- D (vertical shift) = 0
[tex]\implies \large\boxed{y = 2sin(3x)}[/tex]
see graph below for verification
