Find the vertical asymptote(s) of the graph of the function. \( f(x)=\frac{3-x}{(x-4)(x+5)} \)

To find the vertical asymptotes of the function \( f(x)=\frac{3-x}{(x-4)(x+5)} \), we need to determine where the denominator is equal to zero, since vertical asymptotes occur at these points (provided the numerator is not zero at the same points). Setting the denominator equal to zero: \[ (x-4)(x+5) = 0 \] This gives us two equations to solve: 1. \( x - 4 = 0 \) → \( x = 4 \) 2. \( x + 5 = 0 \) → \( x = -5 \) Thus, the vertical asymptotes are at \( x = 4 \) and \( x = -5 \). At these values, the function goes to positive or negative infinity, creating those vertical lines on the graph!