Athermal, tethered chains are modeled with density functional (DFT) theory for both the explicit solvent and continuum solvent cases. The structure of DFT is shown to reduce to self-consistent-field theory in the incompressible limit where there is symmetry between solvent and monomer, and to single-chain-mean-field (SCMF) theory in the continuum solvent limit. We show that by careful selection of the reference and ideal systems in DFT theory, self-consistent numerical solutions can be obtained, thereby avoiding the single chain Monte Carlo simulation in SCMF theory. On long length scales, excellent agreement is seen between the simplified DFT theory and molecular dynamics simulations of both continuum solvents and explicit-molecule solvents. In order to describe the structure of the polymer and solvent near the surface it is necessary to include compressibility effects and the nonlocality of the field.