Final answer:
The graph of the function y = cos(4x) is a cosine wave with a period of π/2 radians and oscillates between +1 and -1. The wave completes a full cycle four times as quickly as the standard cosine wave because of the multiplier of 4 on the variable x.
Step-by-step explanation:
The question asks which graph represents the function y = cos(4x). To determine the graph of this function, we consider the characteristics of the cosine function and how they are affected by the factor of 4 multiplying the variable x.
The cosine function, y = cos(x), typically has a period of 2π radians, a maximum value of 1, and a minimum value of -1. When the function is transformed to y = cos(4x), the period becomes 2π/4 or π/2 radians, because the factor of 4 causes the cosine wave to complete a full cycle four times more quickly than the standard cosine function.
In a graph representing y = cos(4x), we would expect to see a wave that reaches its maximum and minimum values within a shorter x-interval than a standard cosine wave. This is due to the increased frequency of oscillation. The amplitude remains the same, between -1 and 1, since there is no coefficient affecting the amplitude of the cosine function.
When plotting the graph of y = cos(4x), you would start at (0,1) since the cosine of 0 is 1, and then plot subsequent peaks and troughs at intervals of π/2 radians along the x-axis. This results in a wave-like shape that oscillates between +1 and -1, with a compressed cycle compared to the standard cosine function.