1. The problem asks to write the equation of the periodic function based on the graph. 2. The graph shows a cosine wave with amplitude 4, oscillating between 4 and -4, and a period of $2\pi$. The wave starts at $y=4$ when $x=0$. 3. The general form of a cosine function is: $$y = A \cos(x)$$ where $A$ is the amplitude. 4. Since the amplitude is 4 and the wave starts at $y=4$ when $x=0$, the function is: $$y = 4 \cos(x)$$ 5. The negative options or sine options do not match the starting point or amplitude of the graph. Final answer: $$y = 4 \cos(x)$$