Graph a function with frac

This can be done using the package tikz. The following code shows how you can draw (any) graph using this package.

documentclass[12pt]{report}

usepackage{tikz}

begin{document}

begin{tikzpicture}
  draw [gray,dotted] (0,-6) grid (10,7) ;
  draw[->,>=latex] (0,0) -- (10,0) node[below]{$s$} ;
  draw[->,>=latex] (0,-6) -- (0,7) node[left]{$f(s)$} ;

  draw [domain=0:10,samples=200] plot (x,{(x^3+7*(x)^2+9*x-128)/((x)^2+15*x+24}) ;
end{tikzpicture}

end{document}

This graph is drawn in the domain [0,10] with 200 samples. This can be adjusted according to what domain you want use and how smooth you want the curve to be.