I need to know how to start looking for an equation that has the following asymtope
verticala asymtope x=3 and x=-8
horizontal asymtope y = -3
no oblique
You're going to need a denominator of your rational function to have factors of (x-3)(x+8) to get your vertical asymptotes.
And to get horizontal asymptote of y=-3, make the highest power of x in the numerator and denominator the same (in this case 2) and the coefficient in the numerator should be -3.
So, you get:
$\displaystyle f(x)=\frac{-3x^2}{x^2+5x-24}$