1. **State the problem:** We need to sketch a sinusoidal function with period 8, amplitude 5, axis at $y=-1$, and 2 cycles. 2. **Formula for sinusoidal function:** A general sinusoidal function can be written as $$y = A \sin\left(\frac{2\pi}{T}x\right) + D$$ where $A$ is amplitude, $T$ is period, and $D$ is the vertical shift (axis). 3. **Identify parameters:** - Amplitude $A = 5$ - Period $T = 8$ - Axis $D = -1$ - Number of cycles = 2 (so domain covers $2 \times 8 = 16$ units) 4. **Calculate max and min values:** - Maximum value = $D + A = -1 + 5 = 4$ - Minimum value = $D - A = -1 - 5 = -6$ 5. **Write the equation:** $$y = 5 \sin\left(\frac{2\pi}{8}x\right) - 1 = 5 \sin\left(\frac{\pi}{4}x\right) - 1$$ 6. **Label axes:** - Horizontal axis: "Time" from 0 to 16 (to show 2 full cycles) - Vertical axis: "height" from -6 to 4 7. **Summary:** The sinusoidal wave oscillates between -6 and 4, centered at $y=-1$, with period 8, completing 2 cycles over the interval $[0,16]$. This completes the problem.