Determine the equation of a rational function with a hole at x -5 a y-intercept of 0.5 and vertical asymtotes at x -4 and x 2?

To have asymptote -4, put (x + 4) in the denominator. To have asymptote 2, put (x-2) in the denominator. For the hole at -5, put (x+5) in numerator and denominator. So we have:

(x + 5)/((x + 4)(x + 5)(x - 2)), now multiply this by a constant (A), then set x = 0, and solve for A such that y = 0.5.

A(0 + 5)/(4*5*(-2)) = -A/8. So if -A/8 = 1/2, then A = -4.