1. **State the problem:** We are given the function $y = f(x) = \frac{2}{x - 5}$ and need to find its vertical and horizontal asymptotes. 2. **Vertical asymptote:** Vertical asymptotes occur where the denominator is zero because the function is undefined there. Set the denominator equal to zero: $$x - 5 = 0$$ Solve for $x$: $$x = 5$$ So, the vertical asymptote is at $x = 5$. 3. **Horizontal asymptote:** For rational functions where the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is $y = 0$. Since the numerator is a constant (degree 0) and the denominator is degree 1, the horizontal asymptote is: $$y = 0$$ 4. **Summary:** - Vertical asymptote: $x = 5$ - Horizontal asymptote: $y = 0$ This matches the top-right graph described, which has vertical asymptote at $x=5$ and horizontal asymptote at $y=0$ with branches in quadrants II and IV.