1. **State the problem:** We need to find the period of the sinusoidal function based on the graph description. 2. **Recall the period definition:** The period of a sinusoidal function is the horizontal length over which the function completes one full cycle and starts repeating. 3. **Analyze the graph points:** The function has peaks at $-3\pi$ and $\pi$, and troughs at $-\pi$ and $3\pi$. 4. **Calculate the period:** The distance between two consecutive peaks is the period. $$\text{Period} = \pi - (-3\pi) = \pi + 3\pi = 4\pi$$ 5. **Conclusion:** The period of the sinusoidal function is $4\pi$. This means the function repeats every $4\pi$ units along the x-axis.