1. The problem is to find the function $f(x)$ that corresponds to the given sine wave graph. 2. The graph shows a sine wave oscillating between $y = 2$ and $y = -2$, which suggests the amplitude $A = 2$. 3. The x-axis range is from $-8$ to $8$, and the wave completes a full cycle within this range, indicating the period $T = 16$. 4. The general form of a sine function is $$f(x) = A \sin\left(B(x - C)\right) + D,$$ where: - $A$ is the amplitude, - $B = \frac{2\pi}{T}$ is the frequency, - $C$ is the horizontal shift (phase shift), - $D$ is the vertical shift. 5. Since the wave oscillates symmetrically about the x-axis, the vertical shift $D = 0$. 6. Calculate $B$: $$B = \frac{2\pi}{T} = \frac{2\pi}{16} = \frac{\pi}{8}.$$ 7. The wave starts near $x = -8$ at $y = 0$ and goes upward, so there is no horizontal shift, $C = 0$. 8. Therefore, the function is: $$f(x) = 2 \sin\left(\frac{\pi}{8} x\right).$$ 9. This matches the given graph's amplitude, period, and phase. Final answer: $$f(x) = 2 \sin\left(\frac{\pi}{8} x\right).$$