To find the vertical asymptote of the function \( f(x) = \frac{x - 2}{x} \), we need to identify the values of \( x \) that make the denominator zero, as these will be the locations of any vertical asymptotes.

For the function \( f(x) = \frac{x - 2}{x} \), the denominator is \( x \). The vertical asymptote occurs when the denominator is zero:

\[
x = 0
\]

So, the vertical asymptote of the function is at \( x = 0 \).

Would you like further details or have any questions?

Here are some related questions:
1. How do you determine horizontal asymptotes for this function?
2. What is the behavior of the function as \( x \) approaches the vertical asymptote?
3. What is the equation of the horizontal asymptote for \( f(x) = \frac{x-2}{x} \)?
4. How would the function change if the numerator was \( x + 2 \) instead of \( x - 2 \)?
5. What would happen to the vertical asymptote if the function was \( f(x) = \frac{(x-2)}{(x+1)} \)?

**Tip:** When dealing with rational functions, vertical asymptotes occur where the denominator is zero, provided the numerator does not also become zero at the same point.

Learn how to find the vertical asymptote of the function f(x) = (x-2)/x with a detailed explanation. Understand where vertical asymptotes occur in rational functions and how to determine them algebraically. Suitable for Grades 11-12 students and anyone studying rational functions.

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