Graph all vertical and horizontal asymptotes of the rational function. \[ f(x)=\frac{-6 x+11}{-2 x-9} \quad \text { Question } 7 \]

To find the vertical asymptote of the rational function \( f(x) = \frac{-6x + 11}{-2x - 9} \), we set the denominator equal to zero: \(-2x - 9 = 0\). Solving for \(x\), we get: \(-2x = 9 \Rightarrow x = -\frac{9}{2}\). Thus, the vertical asymptote is at \(x = -\frac{9}{2}\). To determine the horizontal asymptote, we compare the degrees of the numerator and denominator. Both have a degree of 1. The horizontal asymptote is found by taking the ratio of the leading coefficients. Thus, we have: Horizontal asymptote \(y = \frac{-6}{-2} = 3\). In summary, the vertical asymptote is at \(x = -\frac{9}{2}\) and the horizontal asymptote is at \(y = 3\).