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The problem here is asking you to determine the equation of a trigonometric function, which appears to be either a sine or cosine function. Let's analyze the provided graph and the general form of the equation.

### Steps to Solve:

1. **Identify the Type of Function**:
   - Since the graph could be a sine or cosine function, let's check for symmetry. A cosine function typically starts at a peak (if it's not phase-shifted) whereas a sine function typically starts at the midline.

2. **Determine Amplitude and Period**:
   - **Amplitude** (\(a\)): The amplitude is the distance from the midline to the peak. From the graph, the peak appears to be at 3 and the trough at -3, giving an amplitude of \( a = 3 \).
   - **Period** (\(b\)): The period of the function can be determined by the horizontal length over which the function repeats. For both sine and cosine, the period \(T\) is related to \(b\) by the formula \(T = \frac{2\pi}{b}\). The period in the graph appears to be \(2\), so we solve for \(b\):
     \[
     2 = \frac{2\pi}{b} \Rightarrow b = \pi
     \]

3. **Determine if it is a Sine or Cosine Function**:
   - Observing the graph, it starts from \(y = 0\) and goes upward, which is characteristic of a sine wave. Therefore, the function is likely \( y = a \sin(bx) \).

4. **Form the Equation**:
   - Plugging in the values of \(a\) and \(b\) we get:
     \[
     y = 3 \sin(\pi x)
     \]

### Final Answer:
The equation of the function is:
\[
y = 3 \sin(\pi x)
\]

Would you like any further clarification or details on this solution?

Here are 5 related questions to explore further:
1. How does the phase shift affect the equation of a sine or cosine function?
2. What are the steps to find the period of a transformed trigonometric function?
3. How can you tell the difference between a sine and cosine graph just by looking at it?
4. How do amplitude and frequency affect the appearance of sine and cosine waves?
5. What is the impact of a vertical shift on a trigonometric graph?

**Tip**: To distinguish between sine and cosine functions quickly, remember that cosine waves generally start from a maximum or minimum point, while sine waves typically start from the midline.

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 trigonometric graph of the form y = a sin(bx) or y = a cos(bx). This solution involves identifying amplitude, period, and distinguishing between sine and cosine graphs.

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