The graph of the function $y = \cos \left( x - \frac{\pi}{12} \right)$ is shown above. It depicts the cosine wave, shifted to the right by $\frac{\pi}{12}$, over the interval $[-2\pi, 2\pi]$. The wave maintains its typical oscillation between 1 and -1, with critical points shifted accordingly.

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Here are 5 related questions you can explore:

1. How would the graph change if the function was $y = \cos(x + \frac{\pi}{12})$?
2. What effect does modifying the amplitude have on the cosine function?
3. How would the period of the function change if it was $y = \cos(2x)$?
4. Can you describe the graph of $y = \sin\left( x - \frac{\pi}{12} \right)$?
5. What happens to the graph if we introduce a vertical shift, such as $y = \cos\left( x - \frac{\pi}{12} \right) + 1$?

Tip: The phase shift affects the horizontal position of the wave but does not alter the amplitude or period.