1. The problem is to find the horizontal asymptote of the function $$f(x) = \frac{x^2 + 4x - 8}{x - 8}$$. 2. Horizontal asymptotes describe the behavior of a function as $$x \to \pm \infty$$. For rational functions, compare the degrees of numerator and denominator: - If degree numerator < degree denominator, horizontal asymptote is $$y=0$$. - If degrees are equal, horizontal asymptote is $$y = \frac{\text{leading coefficient numerator}}{\text{leading coefficient denominator}}$$. - If degree numerator > degree denominator, no horizontal asymptote (there may be an oblique/slant asymptote). 3. Here, degree numerator = 2, degree denominator = 1, so degree numerator > degree denominator. 4. This means no horizontal asymptote exists. Instead, there is a slant (oblique) asymptote. 5. To find the slant asymptote, perform polynomial division: $$\frac{x^2 + 4x - 8}{x - 8} = x + 12 + \frac{88}{x - 8}$$ 6. As $$x \to \pm \infty$$, $$\frac{88}{x - 8} \to 0$$, so the slant asymptote is $$y = x + 12$$. 7. The question asks for horizontal asymptote, which does not exist here. 8. Therefore, the correct answer is B. None.