Question

question 4
based on the graph above, determine the amplitude, midline, and period of the function
amplitude:
period:
midline: y=
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Explanation:

Step1: Find the amplitude

The amplitude is the distance from the midline to the maximum (or minimum) value. The maximum value is \(1\) and the minimum value is \(-3\). The mid - value between \(1\) and \(-3\) is \(\frac{1+( - 3)}{2}=-1\). The amplitude \(A=\vert1-(-1)\vert = 2\) (or \(\vert-3 - (-1)\vert=2\)).

Step2: Find the period

The period is the length of one full cycle of the function. From \(x=-3\) to \(x = 1\) is one full cycle. So the period \(T=\vert1-(-3)\vert=4\).

Step3: Find the midline

The midline is the horizontal line that the graph oscillates around. We can calculate it as \(y=\frac{\text{max}+\text{min}}{2}\). Here, \(\text{max} = 1\) and \(\text{min}=-3\), so \(y=\frac{1+( - 3)}{2}=-1\).

Answer:

Amplitude: \(2\)
Period: \(4\)
Midline: \(y=-1\)