Graph the function y = –cos(x) + 7 and explain how to find the number of times the gum returns to the wall as it travels a distance of 60 feet.

Answer:

The graph of y = –cos(x) + 7 is a cosine wave reflected across the x-axis with a vertical shift of 7 units. The minimum value of the function is 6 (found at y = -1 + 7), which represents the height of the wall. To find the number of times the gum returns to the wall, count the number of minimum points on the graph for the interval 0 < x ≤ 60. Since the period is 2π ≈ 6.28, you can divide the total distance by the period (60 / 6.28 ≈ 9.55). There are 9 full cycles, meaning the gum returns to the wall 9 times.