Here is the graph of \([ \tan(x) ]\). The horizontal steps represent the integer values that \(\tan(x)\) rounds down to. The red dashed lines indicate the vertical asymptotes where \(\tan(x)\) is undefined.

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Here are 8 related questions:
1. What are the properties of the \(\tan(x)\) function?
2. How does the floor function work with other trigonometric functions?
3. What are the asymptotes of \(\tan(x)\) and why do they occur?
4. Can the graph of \([ \tan(x) ]\) be shifted or stretched?
5. How would the graph change if we used the ceiling function instead of the floor function?
6. What is the behavior of the \(\tan(x)\) function at specific points like \(x = \frac{\pi}{4}\)?
7. What are some applications of the floor function in trigonometry?
8. How would the graph look for a different interval, such as \(0 \leq x \leq 2\pi\)?

**Tip:** Understanding the behavior of the floor function with various functions helps in visualizing piecewise and step functions effectively.

Explore the graph of tan(x) with the floor function applied. Understand how the floor function affects trigonometric graphs, including the presence of asymptotes and stepwise behavior. Learn about the practical applications and variations of using floor functions in trigonometry.

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