Find all horizontal asymptotes of the following function. \[ f(x)=\frac{(x-4)(x-6)}{(x+5)(x+3)} \]

To find the horizontal asymptotes of the function \[ f(x) = \frac{(x-4)(x-6)}{(x+5)(x+3)}, \] we first need to analyze the degrees of the polynomial in the numerator and denominator. The degree of the numerator, \((x-4)(x-6) = x^2 - 10x + 24\), is 2, and the degree of the denominator, \((x+5)(x+3) = x^2 + 8x + 15\), is also 2. When the degrees of the numerator and denominator are equal, the horizontal asymptote is given by the ratio of the leading coefficients of the numerator and denominator. In this case, the leading coefficient of the numerator (the coefficient of \(x^2\)) is 1, and the leading coefficient of the denominator is also 1. Therefore, the horizontal asymptote is: \[ y = \frac{1}{1} = 1. \] Thus, the function has a horizontal asymptote at \[ y = 1. \]