Three different methods, namely maximum entropy, combination of Dirac deltas and two-point Padé approximants, are used to construct tight model-independent approximations to the atomic form factor F(k) in terms of a few quantities related to its inverse Fourier trnsform, i.e. the one-particle density ρ(r). The accuracy of these approximations is analyzed in a Hartree-Fock framework. These extrapolation techniques, being completely general and modelindependent, can be applied to other kind of physical systems, such as solids, molecules or nuclei.