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The problem in your image asks to determine the equation of the given graph, which is in the form \( y = a \sin(bx) \) or \( y = a \cos(bx) \), where \( a \) is the amplitude and \( b \) affects the period.

From the graph:
- The maximum value is \( y = 4 \) and the minimum is \( y = -4 \), so the amplitude \( a \) is \( 4 \).
- The period of the graph is \( 2\pi \). From the graph, the curve completes one cycle between \( 0 \) and \( 2\pi \). The formula for the period of a sine or cosine function is \( \frac{2\pi}{b} \). Given that the period is \( 2\pi \), we can conclude \( b = 1 \).
- Since the graph starts at \( y = 0 \) and has a positive slope, it resembles a sine wave.

Thus, the equation of the graph is:

\[
y = 4 \sin(x)
\]

Let me know if you want further clarification.

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Here are 5 follow-up questions related to this problem:
1. What would happen to the graph if the amplitude \( a \) were doubled?
2. How does the value of \( b \) affect the period of a sine or cosine function?
3. What is the difference in the shape of the graph between \( y = \sin(x) \) and \( y = \cos(x) \)?
4. If the phase shift were added, how would the equation change?
5. How would the graph change if the function were \( y = 4 \cos(x) \) instead?

**Tip:** Always check the period of the function by observing how long it takes for the graph to complete one full cycle.

The function graphed is of the form y = a sin(bx) or y = a cos(bx), where b > 0. Determine the equation of the graph.

Learn how to determine the equation of a graph that represents a trigonometric function of the form y = a sin(bx) or y = a cos(bx). This problem covers key concepts like amplitude and period. Suitable for students in Grades 10-12.

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