graph of tan[x] where [ ] represent greatest integer function 

Here is the graph of \(\tan([x])\). The graph steps at each integer value of \(x\), with the tangent evaluated at those integer points. The green dashed lines mark the steps where the value of \(\tan([x])\) changes.

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Here are 8 related questions:
1. How does the graph of \(\tan([x])\) compare to the graph of \(\tan(x)\)?
2. What happens at the integer points where \(\tan([x])\) changes?
3. How would the graph look if we used \(\sin([x])\) instead?
4. What are the discontinuities in the \(\tan([x])\) function?
5. Can \(\tan([x])\) be used in modeling periodic behavior?
6. How does the step function behavior affect the range of \(\tan([x])\)?
7. What is the effect of applying other transformations to \(\tan([x])\)?
8. How would the graph change if we evaluated \(\tan([x])\) over a different range of \(x\)?

**Tip:** When analyzing piecewise functions like \(\tan([x])\), focus on the behavior at the points of discontinuity to understand the overall shape and pattern of the graph.

Explore the graph of tan([x]) where [ ] represents the greatest integer function. This graph displays step-like behavior at each integer value of x, showcasing changes in the tangent function. Learn about the impact of piecewise functions on trigonometric graphs.

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