To determine the correct equation that represents the graph, let us analyze the given information:

Key Observations:

1. Amplitude: The maximum value is $3.5$ and the minimum value is $-3.5$. Hence, the amplitude ($A$) is $3.5$.
2. Period: The curve repeats itself every $2\pi$, so the period matches a standard sine or cosine function.
3. Behavior at $x = 0$:
   • At $x = 0$, the graph is at its maximum ($3.5$). This is characteristic of a cosine function since cosine typically starts at its maximum at $x = 0$.
4. Positive or Negative:
   • The graph decreases from $x = 0$ to $\frac{\pi}{2}$, indicating it is a positive cosine function.

Equation Form:

The general equation for a cosine function is: $y = A \cos(x)$ Substituting the amplitude $A = 3.5$, the equation becomes: $y = 3.5 \cos(x)$

Answer:

The correct choice is: A. $y = 3.5 \cos(x)$

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Would you like me to explain more about how to identify the equation type or explore related transformations?

Here are 5 follow-up questions to deepen understanding:

1. How would the graph look if the amplitude were halved?
2. What changes to the equation if the graph starts at the minimum instead of the maximum?
3. How can we determine the phase shift of a sine or cosine function?
4. What happens if the period is changed from $2\pi$ to $\pi$?
5. How does adding a vertical shift affect the equation?

Tip: To distinguish between sine and cosine graphs, always check the starting point and compare it to their standard forms.