Question

which graph represents the equation $y = 3\sin\left(\frac{1}{3}x\
ight)$?

Explanation:

Step1: Identify amplitude

For $y = A\sin(Bx)$, amplitude is $|A|$. Here $A=3$, so amplitude $=3$.

Step2: Calculate period

Period formula: $\frac{2\pi}{|B|}$. Here $B=\frac{1}{3}$, so period $=\frac{2\pi}{\frac{1}{3}}=6\pi$.

Step3: Match to graph

The first graph has amplitude 3 (peaks at $y=3$, troughs at $y=-3$) and completes one full cycle over $6\pi$, which matches.

Answer:

The first graph (left-most graph with amplitude 3 and period $6\pi$)