Questions: Determine the amplitude, period, and midline for the graph shown in the figure. Amplitude Period Midline y= Determine an equation for the graph involving the sine function.

Determine the amplitude, period, and midline for the graph shown in the figure. Amplitude Period Midline y= Determine an equation for the graph involving the sine function.
Transcript text: Determine the amplitude, period, and midline for the graph shown in the figure. Amplitude $\square$ Period $\square$ Midline $\square$ $y=$ Determine an equation for the graph involving the sine function. $\square$
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Solution

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Solution Steps

Step 1: Find the amplitude

The amplitude is the distance from the midline to the maximum or minimum value of the function. The maximum value is -2, and the minimum value is -6. The midline is halfway between these values, at $y = \frac{-2 + (-6)}{2} = -4$. The amplitude is the distance from the midline to the maximum or minimum, which is $|-2 - (-4)| = |-2 + 4| = 2$.

Step 2: Find the period

The period is the horizontal distance it takes for the graph to complete one full cycle. One cycle of the sine wave starts at its minimum value $x=-7$ goes to its maximum $x=1$, and comes back to the same minimum value at $x=9$. The distance along x, $9-(-7) = 9+7 =16$, represents one period.

Step 3: Find the midline

The midline is the horizontal line that is halfway between the maximum and minimum values of the function. As calculated in Step 1, the midline is at $y=-4$.

Final Answer:

Amplitude = 2, Period = 16, Midline: $y = -4$

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