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Identify the function whose graph appears above.

The graph you provided appears to resemble the general shape of the tangent function, \( f(x) = \tan(x) \). This is because the graph shows vertical asymptotes at intervals like \( -\frac{3\pi}{2}, -\frac{\pi}{2}, \frac{\pi}{2}, \frac{3\pi}{2} \), which are characteristic of the tangent function.

Additionally, the curve crosses the x-axis at points like \( 0, \pi, 2\pi \), which matches the zeros of the tangent function. Based on these observations, the function is likely:

\[
f(x) = \tan(x)
\]

Would you like further details on how this conclusion was reached or how the tangent function behaves?

Here are five related questions to consider:
1. How does the tangent function differ from sine and cosine in terms of asymptotes?
2. What transformations can be applied to the basic tangent graph, such as stretching or shifting?
3. What is the period of the tangent function, and how does it compare to other trigonometric functions?
4. Why do tangent graphs have vertical asymptotes, and how can you predict their locations?
5. How can you modify the tangent function to reflect changes in amplitude or phase?

**Tip:** Vertical asymptotes in graphs often signal functions like tangent or cotangent, which are undefined at certain points.

Learn how to identify the graph of the tangent function f(x) = tan(x) by analyzing its vertical asymptotes and zeros. This trigonometry problem is suitable for students in Grades 10-12 and covers the key properties of the tangent function.

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