https://file.aiquickdraw.com/mathbot/file/17290241565600j1f1l81.jpg

To determine which graph represents a function with amplitude 4 and period \( \pi \), let's break down the information:

1. **Amplitude**: The amplitude is the maximum value of the function from its midline. A function with amplitude 4 will oscillate between -4 and 4.

2. **Period**: The period is the horizontal distance required for the function to complete one full cycle. A function with a period of \( \pi \) repeats itself every \( \pi \) units along the x-axis.

### Analysis of the Graphs:
- The first graph oscillates between -5 and 5, so its amplitude is not 4.
- The second graph appears to oscillate between -4 and 4, and the distance between peaks looks like \( \pi \), indicating a period of \( \pi \).
- The third graph has an amplitude of 4, but the period appears to be longer than \( \pi \).
- The fourth graph seems to oscillate between -5 and 5, so its amplitude isn't correct.

### Conclusion:
The **second graph** represents a function with amplitude 4 and period \( \pi \).

Would you like further details on how to calculate the period or amplitude, or do you have any other questions?

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Here are five related questions:
1. What is the general form of a sine or cosine function in terms of amplitude and period?
2. How can the period of a trigonometric function be adjusted using its equation?
3. What effect does changing the amplitude have on the graph of a sine or cosine function?
4. How can you determine the phase shift of a trigonometric function from its graph?
5. How do you calculate the frequency of a function if you know its period?

**Tip**: The period of a sine or cosine function can be determined by dividing \( 2\pi \) by the coefficient of \( x \) in the function \( f(x) = A \sin(Bx) \) or \( f(x) = A \cos(Bx) \).

Which graph represents a function with amplitude 4 and period π?

Learn how to identify the graph of a trigonometric function with an amplitude of 4 and a period of π. This problem explains key concepts in trigonometry, including how to find amplitude and period for sine and cosine functions, and is suitable for high school students.

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