Question

standard 15 homework
score: 8/21 answered: 8/20
question 10
determine the amplitude, midline, and period of the function shown above.
the amplitude is
the period is
the midline is ( y = )

Explanation:

Step1: Find the amplitude

The amplitude of a sinusoidal function is half the distance between the maximum and minimum values.
The maximum value \(y = - 2\), the minimum value \(y=-6\).

$$
LATEXBLOCK0
$$

Step2: Find the mid - line

The mid - line of a sinusoidal function is the average of the maximum and minimum values.

$$
LATEXBLOCK1
$$

Step3: Find the period

The period is the horizontal length of one complete cycle of the function.
From the graph, one complete cycle occurs from \(x=-3\) to \(x = 1\) (a distance of \(4\) units).

Answer:

The amplitude is \(2\).
The period is \(4\).
The midline is \(y=-4\).