The rational function \( r(x)=\frac{(x+3)(x-1)(x+4)}{(x-5)(x+3)(x-4)} \) has - Zeros (x-intercepts) at \( x=1,-4 \) - Vertical asymptotes at \( x=\square \) - A hole at \( x= \) - A horizontal asymptote at \( y=\square \)

The vertical asymptotes occur where the function is undefined, specifically at the values of \( x \) that make the denominator zero but not the numerator. Here, the denominator has \( (x-5)(x+3)(x-4) \), so vertical asymptotes are at \( x=5 \) and \( x=-3 \). Now, for the hole, it appears at \( x = -3 \) because the \( (x+3) \) factor cancels out in both the numerator and the denominator. Finally, the horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator. Since both the numerator and denominator are of degree 3, the horizontal asymptote is determined by the leading coefficients. Here, it is \( y=1 \).