1. The problem is to explain how the vertical and horizontal asymptotes of the function $$f(x) = \frac{22x - 3}{x + 13}$$ are found. 2. **Vertical asymptote:** This occurs where the denominator is zero because the function is undefined there. Set the denominator equal to zero: $$x + 13 = 0$$ Solve for $$x$$: $$x = -13$$ So, the vertical asymptote is at $$x = -13$$. 3. **Horizontal asymptote:** For rational functions where the degree of the numerator and denominator are the same (both degree 1 here), the horizontal asymptote is the ratio of the leading coefficients. The leading coefficient of the numerator is 22, and the leading coefficient of the denominator is 1. Therefore, the horizontal asymptote is: $$y = \frac{22}{1} = 22$$ 4. This means as $$x \to \pm \infty$$, $$f(x) \to 22$$. 5. In summary: - Vertical asymptote at $$x = -13$$ because the denominator is zero there. - Horizontal asymptote at $$y = 22$$ because the degrees of numerator and denominator are equal and the asymptote is the ratio of leading coefficients. This explains how the asymptotes were found for the function.