Find all horizontal and vertical asymptotes of \( f(x) \). \( f(x)=\frac{4 x^{2}+11 x-3}{x^{2}+3 x-18} \) Find the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choi A. The function has one horizontal asymptote, (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is \( \square \) and the bottom asymptote is (Type equations.) The function has no horizontal asymptotes.

To find the horizontal asymptotes of the function \( f(x) = \frac{4x^2 + 11x - 3}{x^2 + 3x - 18} \), we compare the degrees of the polynomial in the numerator and the denominator. Both the numerator and denominator are quadratic polynomials (degree 2). When the degrees of the numerator and denominator are equal, the horizontal asymptote is given by the ratio of the leading coefficients. The leading coefficient of the numerator (4) and the leading coefficient of the denominator (1) yield: \[ y = \frac{4}{1} = 4 \] Thus, there is one horizontal asymptote: **The function has one horizontal asymptote,** \(y = 4\). For the vertical asymptotes, we find the values of \(x\) that make the denominator zero. Setting the denominator \(x^2 + 3x - 18 = 0\) allows us to factor it: \[ (x + 6)(x - 3) = 0 \] This gives us two vertical asymptotes at: \[ x = -6 \quad \text{and} \quad x = 3 \] In summary, the function has one horizontal asymptote at \(y = 4\) and vertical asymptotes at \(x = -6\) and \(x = 3\).