relating maximum, minimum, amplitude, and equation\ncomplete the following statements for the cosine…

Explanation:

Step1: Identify minimum value

By observing the graph, the lowest - point on the cosine function has a (y) - value of (-1).

Step2: Identify maximum value

The highest - point on the cosine function has a (y) - value of (1).

Step3: Calculate amplitude

The amplitude (A) of a periodic function is given by (A=\frac{\text{max}-\text{min}}{2}). Here, (\text{max} = 1) and (\text{min}=-1), so (A=\frac{1 - (-1)}{2}=\frac{2}{2}=1).

Step4: Determine the equation

The general form of a cosine function is (y = A\cos(Bx - C)+D). Since (A = 1), (B = 1) (because the period (T = 2\pi=\frac{2\pi}{B}), so (B = 1)), (C = 0) (no phase - shift), and (D = 0) (no vertical shift), the equation is (y=\cos(x)).

Answer:

The minimum value is (-1). The maximum value is (1). The amplitude is (1). An equation for this function is (y = \cos(x)).