Here is the graph of the function $y = 4\cos(x - \pi) + 3$. The cosine wave is shifted to the right by $\pi$ units and shifted up by 3 units. The amplitude of the wave is 4, so it oscillates between -1 and 7.

Do you need any further details or have any questions?

Here are some related questions you might find interesting:

1. How does changing the amplitude affect the graph of a cosine function?
2. What happens if you change the horizontal shift in the cosine function?
3. How would the graph look if the function were $y = 4\sin(x - \pi) + 3$ instead?
4. What are the key points you would use to sketch this graph by hand?
5. How does the period of the function influence the graph?

Tip: When graphing trigonometric functions, always consider the amplitude, period, phase shift, and vertical shift to understand how the graph will behave.