Here is the graph of the cosine function with an amplitude of 2 and a period of $4\pi$.

Would you like any details or explanations regarding this graph?

Here are 5 related questions to deepen your understanding:

1. How does changing the amplitude affect the shape of the cosine graph?
2. What happens to the graph if we change the period to $2\pi$ instead of $4\pi$?
3. How would the graph change if the function was $y = -2 \cos\left(\frac{\pi x}{2}\right)$?
4. How can we determine the phase shift in a cosine function?
5. What is the difference between the graphs of sine and cosine functions with the same amplitude and period?

Tip: The amplitude of a trigonometric function affects the height of the peaks and troughs, while the period affects how "stretched" or "compressed" the wave looks along the x-axis.