The sum, product, and ratio of rational functions are again rational functions, as are constants and x. Therefore, 1) is a rational function.

In 2), do you mean f(t)? Note that the cubic root is not a rational function.

I am not sure how to parse 3): is it (Gr / (r^3)) - 8? Then why not (G / r^2) - 8? Or is it Gr / (r^3 - 8)? Also, I guess it should be f(r). In any case, the same reasoning as in 1) applies.