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.

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.