Graph the trigonometric function f(x) = 2 cos(0.5x) + 2 sin(0.5x). (a) What does the graph initially look like? Now vary d and note the effect on the graph of f. What happens when d = 2b? When d=3b? When d = 4b? This answer has not been graded yet. (b) Set d = 2 and vary a. What is the effect on the graph of f? Changing a has no affect on the graph of f. The graph of f will have the same number of peaks and valleys, but as a changes, the heights of the peaks and valleys change. The graph of f is vertically shifted when a changes. The graph of f is horizontally shifted when a changes. The number of peaks and valleys in the graph of f changes as a changes. How does the graph differ when a < 0? This answer has not been graded yet. Do you see similar changes in the graphs of f' and f"? The changes to the graphs of f' and f" are identical to the changes in the graph of f. Similar changes in the graphs of f' and f" are observed but the degree of change is more obvious for f' and even more obvious for f". The changes to the graph of f" are similar to the changes in the graph of f, but the changes to the graph of f' are not. Similar changes in the graphs of f' and f" are observed but the degree of change is less obvious for f' and even less obvious for f". The changes to the graphs of f' and f" are in no way similar to the changes in the graph of f. How does the graph change if you vary c? What is the effect on the graphs of f' and f"?