the function hits the x axis and bounces up at x=1, so (x-1) has the behavior of an even factor there.
the function goes through the x axis at x=-2, so (x+2) has the behavior of an odd factor.
I'm not sure about the rest
x=-2 and x= 1 are the zeroes of the graph, so (x+2) and (x-1) are factors of the numerator. x=-3 and x=4 are vertical asymptotes of the graph, so (x+3) and (x-4) are factors of the denominator. y=3 is a horizontal asymptote, so we know the top and bottom of the equation have the same degree.
I know the equation takes on this form [ 3*(x+2)*(x-1) ] / [ (x+3)*(x-4) ]
I just don't know to what power each of the factors is raised to like (x+2)^a