We identified a transversing physical connection between kinetic, exchange, and correlation functionals by using parameter-free (Pfree) exchange and one-parameter progressive (OP) correlation. On the basis of this connection, we investigated how the calculated energies and chemical properties depend on the shape of the functional in the Kohn-Sham scheme. We found that the fundamental conditions of the functionals are connected through Pfree and OP functionals with the exception of a rapidly varying density limit. We also found that the calculated properties are highly affected by the exchange functional shape in particular regions of x(sigma)=\del rho (\)/rho (4/3)(sigma).