To clarify, a vertical asymptote occurs when the function's value approaches infinity or negative infinity as the input variable approaches a specific value. This typically happens at values of the independent variable (e.g., $x$) where the function becomes undefined due to division by zero or other undefined operations.

For example:

1. For rational functions like $f(x) = \frac{1}{x - a}$, a vertical asymptote exists at $x = a$ because the denominator becomes zero.

2. For trigonometric functions like $f(x) = \tan(x)$, vertical asymptotes occur where the function is undefined, such as at $x = \frac{\pi}{2} + n\pi$, where $n \in \mathbb{Z}$.

Steps to Determine a Vertical Asymptote:

1. Identify the points where the denominator is zero. For a rational function $\frac{P(x)}{Q(x)}$, find $x$ where $Q(x) = 0$, provided $P(x) \neq 0$ at those points.

2. Check the limits: Verify whether the function approaches infinity ($+\infty$ or $-\infty$) as $x$ approaches the suspected points.

3. Exclude holes: If $Q(x) = 0$ and $P(x) = 0$ at the same point, the discontinuity might be a removable hole, not an asymptote.

Could you provide the function or context you're referring to? That would help determine the vertical asymptote more accurately.

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Follow-Up Questions:

1. What function or equation are you analyzing for vertical asymptotes?
2. Are there other discontinuities (e.g., holes or oblique asymptotes) in your problem?
3. Have you checked for symmetry in the function? Symmetry often reveals patterns in asymptotes.
4. Is this function part of a graphing exercise or a calculus application?
5. Do you need help finding horizontal or oblique asymptotes?

Tip: Always check the limits of the function as $x \to a$ to confirm the presence of an asymptote,