Identify the asymptotes of the graph of \( f(x)=\frac{-6 x-1}{x-9} \) The vertical asymptote is The horizontal asymptote is

To find the vertical asymptote of the function \( f(x)=\frac{-6 x-1}{x-9} \), we set the denominator equal to zero: \( x - 9 = 0 \). This gives us the vertical asymptote at \( x = 9 \). Next, to determine the horizontal asymptote, we look at the degrees of the polynomial in the numerator and the denominator. Here, both the numerator and denominator are degree 1. The horizontal asymptote is found by taking the leading coefficients of both polynomials: \( \frac{-6}{1} = -6 \). Thus, the horizontal asymptote is \( y = -6 \).