Well its deff not continuous at r = 0. What bout r= R? Those should be your 2 checks. Continuity is having the limits approaching from the left and right be equal and defined. So... should be straightforward
The gravitatonal force exerted by the Earth on a unit mass at a distance r from the center of the planet is
F(r) = GMr/R^3 if r<R
F(r)= GM/r^2 if R >/= R
Where M is the mass of the earth, R is its radius, and G is the gravitational constant. Is F a continuous function of r?