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Write an equation of the function that is graphed.

The graph shown is characteristic of a **tangent** or **cotangent** function due to its periodic vertical asymptotes and the general shape of the curve. In particular, this graph appears to be that of the **cotangent function** due to the vertical asymptotes and decreasing behavior from left to right.

The vertical asymptotes are located at multiples of \(\pi\), such as \(-\pi\), \(\pi\), and so on. The graph passes through the origin, and this is typical of a standard cotangent function.

Thus, the general equation for the function graphed is:

\[
y = \cot(x)
\]

### Verifying:

- **Period**: The period of the cotangent function is \(\pi\), which matches the distance between asymptotes.
- **Asymptotes**: The vertical asymptotes at \(-\pi\), \(\pi\), etc., align with the standard cotangent function.
- **Shape**: The graph decreases from left to right between the vertical asymptotes, which is consistent with the cotangent function's behavior.

Therefore, the equation of the function is:

\[
y = \cot(x)
\]

Would you like any further details or explanations? Here are some related questions for further exploration:

1. How is the graph of \(\cot(x)\) different from that of \(\tan(x)\)?
2. What are the vertical asymptotes of the \(\tan(x)\) function?
3. How would you modify the equation to shift the graph horizontally?
4. What is the domain of the cotangent function?
5. How does the amplitude of a cotangent function differ from other trigonometric functions?

**Tip**: To shift the graph horizontally, you can adjust the phase of the function. For instance, \(y = \cot(x - \pi/4)\) shifts the graph \(\pi/4\) units to the right.

Learn how to identify and write the equation of a cotangent function from its graph. This problem explores the key characteristics of the cotangent function, including its periodic asymptotes and behavior between intervals. Suitable for high school students in Grades 10-12.

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