Final answer:
The amplitude of the function y = -3cos(1/4x) is 3 and the period is 8π. The equation of the midline is y = 0.
Step-by-step explanation:
To determine the amplitude and period of the function y = -3cos(1/4x), we can use the general form of a cosine function: y = Acos(Bx - C) + D. In this case, A represents the amplitude, B represents the frequency, C represents the phase shift, and D represents the midline.
Comparing the given function to the general form, we can see that the amplitude is 3, as it is the absolute value of the coefficient in front of the cosine function. The period of the function can be found using the formula T = 2π/B. The coefficient of x in the given function is 1/4, so B = 1/4. Substituting this into the formula, we get T = 2π/(1/4) = 8π.
Finally, to find the equation of the midline, we look at the constant term in the given function. In this case, there is no constant term, so the midline is the x-axis, or y = 0.