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based on the graph above, determine the amplitude, midline, and period of the function
amplitude:
period:
midline: $y=$
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Explanation:

Step1: Calculate the amplitude

The amplitude is half the distance between the maximum and minimum values. The maximum value is \(2\) and the minimum value is \(-4\). The distance between them is \(2 - (-4)=6\). So the amplitude \(A=\frac{6}{2} = 3\).

Step2: Calculate the period

The period is the length of one full cycle of the function. From the graph, one full cycle (e.g., from \(x=-5\) to \(x = - 1\)) has a length of \(4\).

Step3: Calculate the mid - line

The mid - line is the average of the maximum and minimum values. Using the formula \(y=\frac{\text{Max}+\text{Min}}{2}\), we substitute Max \( = 2\) and Min \(=-4\). So \(y=\frac{2+( - 4)}{2}=\frac{-2}{2}=-1\).

Answer:

Amplitude: \(3\)
Period: \(4\)
Midline: \(y=-1\)