Final answer:
The graph of y = 4cos(x) is represented by option c. Option c: y = 4cos(x) has standard cosine function characteristics.
Step-by-step explanation:
The graph of the function y = 4cos(x) is given by option c.
The cosine function is a periodic function with a range of [-1, 1]. When the coefficient of x is 1, the period of the function is 2π. So, when the coefficient of x is 2, the period of the function is π. Therefore, the graph of y = 4cos(2x) will have a shorter period compared to the graph of y = 4cos(x).
Option d, y = -4cos(x), represents a reflection of the graph of y = 4cos(x) about the x-axis.
The correct option is indeed c, where y = 4cos(x). The cosine function, with a coefficient of 1, has a standard period of 2π. When this coefficient becomes 2, as in y = 4cos(2x), the period is reduced to π, resulting in a faster oscillation. Option d,(y = -4cos(x), signifies a reflection about the x-axis, changing the amplitude but not the period. Thus, option c, with the standard cosine function, correctly represents a graph with a period of 2π and amplitude of 4. The given explanations highlight the significance of coefficients on the period and amplitude of trigonometric functions.