The problem asks for the vertical asymptote of the rational function $f(x) = \frac{2x + 3}{x - 1}$.

Vertical Asymptote:

A vertical asymptote occurs where the denominator of a rational function equals zero (as long as the numerator does not also equal zero at the same point).

Given the function $f(x) = \frac{2x + 3}{x - 1}$, the denominator is $x - 1$.

To find the vertical asymptote, set the denominator equal to zero and solve for $x$:

$x - 1 = 0$

$x = 1$

Thus, the vertical asymptote is at $x = 1$.

Conclusion:

The correct answer is option $i$, $x = 1$.

Would you like more details or have any further questions?

Here are 8 related questions you might find useful:

1. How do you find horizontal asymptotes for rational functions?
2. What are slant (oblique) asymptotes, and when do they occur?
3. How do you determine the holes in a rational function?
4. How do you analyze the end behavior of rational functions?
5. Can a rational function have more than one vertical asymptote?
6. What happens to the graph of a function near a vertical asymptote?
7. How do you find the intercepts of a rational function?
8. How does the degree of the numerator and denominator affect the asymptotes?

Tip: When solving for vertical asymptotes, always check for any factors that could cancel out in the numerator and denominator, which might indicate a hole instead of an asymptote.