Here is the graph of the function $y = -\tan\left(\frac{\pi x}{2} + \frac{\pi}{4}\right)$, with the first three vertical asymptotes shown as dashed red lines at $x = 0.5$, $x = 2.5$, and $x = 4.5$.

Would you like further details or have any questions?

Here are five related questions you might find interesting:

1. How do you determine the period of a tangent function?
2. What happens to the function as $x$ approaches an asymptote?
3. How does the negative sign in front of the tangent function affect its graph?
4. Can you explain how phase shifts affect trigonometric functions?
5. What are the differences between the graphs of sine, cosine, and tangent functions?

Tip: Asymptotes represent values where a function is undefined, often causing the function to approach infinity!