Let #x^3+9=p(x)# and #9x=q(x)# #therefore f(x)=(p(x))/(q(x))#
#f(x)# can be expressed in the form of a rational fraction therefore it is a rational function. #p(x)# matches the condition of having a leading coefficient of #1#. #p(x)# and #q(x)# share no common factor.