Here is the graph of $y = \tan(\pi x)$, displaying the characteristic vertical asymptotes where the function is undefined. These occur at points where $x = \frac{k}{2}$ for any integer $k$, as $\tan(\pi x)$ tends to infinity.

Would you like further details or have any questions about this graph?

Here are some related questions that might interest you:

1. How does the period of $\tan(\pi x)$ compare to the standard $\tan(x)$?
2. What causes the asymptotes in $y = \tan(\pi x)$, and how do they differ from other trigonometric functions?
3. How does modifying the coefficient of $x$ within $\tan(kx)$ affect the graph?
4. Can we determine the x-intercepts of $y = \tan(\pi x)$ analytically?
5. How would adding a vertical shift affect the graph of $y = \tan(\pi x)$?

Tip: When graphing trigonometric functions with asymptotes, setting the y-limits can help in visualizing the periodic nature without extreme spikes due to the asymptotes.