Final Answer:
Given f(x) = 3/5 * cos(6x).
Step-by-step explanation:
The function f(x) = 3/5 * cos(6x) represents a cosine function with an amplitude of 3/5 and a frequency of 6, determined by the coefficient of x. The amplitude modifies the vertical stretch or compression of the cosine graph, while the frequency controls the number of oscillations within the unit interval. In this case, the amplitude is 3/5, meaning the function's values range from -3/5 to 3/5. The frequency of 6 indicates that the cosine graph completes six full cycles within the interval 0 ≤ x ≤ 2π.
To understand the behavior of the cosine function, it's essential to recognize the standard form y = A * cos(Bx), where A is the amplitude and B is the frequency. In our function, A = 3/5 and B = 6. The general graph of y = cos(x) oscillates between -1 and 1, but A modifies this range. In this case, the function oscillates between -3/5 and 3/5 due to the amplitude adjustment. Additionally, the frequency of 6 increases the number of oscillations, making the graph complete six cycles for each unit interval.
In conclusion, understanding the properties of the given function involves interpreting the amplitude and frequency within the context of a cosine graph. The provided information facilitates the visualization and analysis of the graph's behavior over the specified interval.