1. The problem is to find the center (midline) of the sinusoidal function $f(x)$ which oscillates between $-2.0$ and $2.0$ on the y-axis. 2. The center or midline of a sinusoidal function is the average of its maximum and minimum values. 3. The formula for the midline $C$ is: $$C = \frac{\text{max} + \text{min}}{2}$$ 4. Given the maximum value $\text{max} = 2.0$ and minimum value $\text{min} = -2.0$, substitute these into the formula: $$C = \frac{2.0 + (-2.0)}{2} = \frac{0}{2} = 0$$ 5. Therefore, the center (midline) of the sinusoidal function $f(x)$ is $0$. This means the sinusoidal curve oscillates symmetrically about the horizontal line $y=0$.