Separating sets by Darboux Baire 1 and approximately continuous functions

We characterize sets A₀, A₁ for which there is a DB1 function f with f = 0] = A₀ and f = 1] = A₁. This characterization is a conjunction of necessary conditions for Darboux and for Baire 1 functions. We also characterize sets A^?, A⁺ for which there is a DB₁ function with f < 0] = A^? and f > 0] = A⁺. The same characterzations are provided for approximately continuous functions.