Question 1128113
Since {{{f}}} has a vertical is at {{{x =-3}}}, and {{{x=6}}} then the denominator of the rational function contains the term {{{(x +3)}}} and {{{x-6}}}. 

Function {{{f}}} has the form. 


{{{f(x) = g(x) / ((x+3) (x-6))}}}

since  has a horizontal asymptote {{{y=-2}}}, x-intercepts {{{(x+4)}}} and {{{(x-1)}}},  {{{g(x)}}} contains 

{{{f(x) = (-2(x+4) (x-1)) / ((x+3) (x-6))}}}


{{{drawing ( 600, 600, -15, 15, -15, 15,line(-3,14,-3,-14),line(6,14,6,-14),
graph( 600, 600, -15, 15, -15, 15,-2,-2((x+4)(x-1)) /((x+3)(x-6)) )) }}}