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?

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 $f(x) = A \cos(Bx)$.