If you would like to still help I have some more that I am working on. Here are the stipulations.

the limit as x appraches negative infinity=-1

the limit as x approaches -2 from the negative= infinity

the limit as x approaches -2 from the positive= negative infinity

the limit as x approaches 2= infinity

the limit as x approaches infinity=-1

x intercepts only at x=4,0,-3

verticle asymptotes at x=-2,2