complete the following to analyze the graph shown. the graph follows the pattern for the sine function…

Explanation:

Step1: Identify the function type

The graph follows the sine - function pattern starting at the origin, so it is a sine - type function of the form (y = a\sin(bx - c)+k).

Step2: Determine the value of (a)

Since the graph starts at the origin and has the general shape of (y = \sin x), (a>0).

Step3: Find the maximum and minimum values

From the graph, the maximum value is (4) and the minimum value is (- 4).

Step4: Calculate the amplitude

The amplitude (|a|) is given by (\frac{\text{max}-\text{min}}{2}). So, (|a|=\frac{4 - (-4)}{2}=\frac{8}{2}=4).

Step5: Determine the vertical translation

The mid - line of the graph is (y = 0), so the vertical translation (k = 0).

Answer:

a is positive; The maximum value is 4; The minimum value is - 4; The amplitude of the function, (|a|), is 4; The vertical translation is (k = 0)