Let's analyze the graph to determine the amplitude, period, and midline.

1. Amplitude: The amplitude is the distance from the midline to the peak (or trough) of the wave. Observing the graph, the maximum value of the function is 3, and the minimum value is -6. The amplitude is half the distance between these values: $\text{Amplitude} = \frac{\text{max value} - \text{min value}}{2} = \frac{3 - (-6)}{2} = \frac{9}{2} = 4.5$

2. Period: The period is the horizontal distance over which the function repeats. From the graph, the function repeats from $x = -5$ to $x = 1$, or from $x = -3$ to $x = 3$. The distance between these points is 6, so the period is 6 units.

3. Midline: The midline is the average of the maximum and minimum values, which defines the horizontal axis around which the function oscillates: $\text{Midline} = \frac{\text{max value} + \text{min value}}{2} = \frac{3 + (-6)}{2} = \frac{-3}{2} = -1.5$

Summary:

• Amplitude: 4.5
• Period: 6
• Midline: $y = -1.5$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you calculate the frequency of a periodic function?
2. What is the general form of a sinusoidal function?
3. How can you shift a sinusoidal function horizontally or vertically?
4. What is the phase shift, and how can it be determined from the graph?
5. How does the amplitude affect the graph of a trigonometric function?

Tip: Always check both the maximum and minimum values carefully when determining the amplitude and midline.