Let's analyze the graph to determine the amplitude, period, and midline of the function:

1. Amplitude: The amplitude is the vertical distance between the midline and the maximum or minimum value of the function.

   • The maximum value on the graph is 6.
   • The minimum value on the graph is -4.
   • The amplitude is half the difference between the maximum and minimum values: $\text{Amplitude} = \frac{\text{Max} - \text{Min}}{2} = \frac{6 - (-4)}{2} = \frac{10}{2} = 5$

2. Midline: The midline is the horizontal line that runs midway between the maximum and minimum values.

   • The midline can be calculated as the average of the maximum and minimum values: $\text{Midline} = \frac{\text{Max} + \text{Min}}{2} = \frac{6 + (-4)}{2} = \frac{2}{2} = 1$ So, the equation of the midline is $y = 1$.

3. Period: The period is the horizontal length of one complete cycle of the wave.

   • From the graph, one cycle starts at $x = -4$ and completes at $x = 4$, so the period is: $\text{Period} = 4 - (-4) = 8$

Final Answers:

• Amplitude: 5
• Period: 8
• Midline: $y = 1$

Would you like any more details or further clarification?

Here are 5 related questions:

1. How is the formula for amplitude derived for different types of waves?
2. What would happen to the function if the amplitude doubled?
3. How do you calculate the frequency from the period?
4. How does the graph change if the midline shifts up by 3 units?
5. Can you determine the equation of the sinusoidal function from this graph?

Tip: Always check the vertical range of the graph to easily determine the amplitude and midline of periodic functions!