Question

Write an equation for a rational function with:

Answer 1

Making a fraction is the easiest way to do this.

The x-intercepts give solutions to a problem that equals zero.
$0 = (x-5)(x+1)$
The vertical asymptotes are values x cannot be, in a fraction the denominator can not be zero.
$y = \frac{(x-5)(x+1)}{(x+4)(x-3)}$
Horizontal asymptotes are the values y approaches. This can be accomplished by making the leading term have a coefficient of 6
$y = \frac{6(x-5)(x+1)}{(x+4)(x-3)}$