Integrating graphene into electronic devices requires support by a substrate and contact with metal electrodes. Ab initio calculations at the level of density functional theory are performed on graphene-fcc-metal(111) [Gr/M(111)] (M = Ni, Cu, Au) systems. The strongly constrained and appropriately normed (SCAN) and SCAN with the revised Vydrov-van Voorhis (SCAN+rVV10) functionals are relatively new approximations to the exchange-correlation (xc) energy shown to account for van der Waals (vdW) interactions which many non-empirical semi-local functionals fail to include. Binding energies and distances as well as electronic band structures are calculated with SCAN, SCAN+rVV10, Perdew-Burke-Ernzerhof (PBE), and PBE-D3 with and without Becke-Johnson damping, Bayesian error estimation functional with van der Waals correlation (BEEF-vdW), and optB86b-vdW. SCAN and SCAN+rVV10 succeed in describing chemisorption and physisorption in the Gr/Ni(111) system and physisorption in the Gr/Cu(111) and Gr/Au(111) systems. Incorrectly, the physisorption is found to be more favorable than chemisorption in the Gr/Ni(111) system with SCAN, but the result is reversed when the experimental bulk Ni lattice parameter is used as opposed to the SCAN calculated lattice parameter. The SCAN+rVV10 functional produces binding energies and distances comparable to those calculated using the random phase approximation as well as the experiment. The SCAN based functionals produce the highest spin magnetic moments in the bulk Ni and Gr/Ni(111) systems compared to the rest of the functionals investigated, overestimating the experiment by at least ∼0.18 μB. Also, in contrast to the rest of the functionals, the induced spin magnetic moment in graphene is found to be larger in magnitude in the physisorption region than the chemisorption region. The pristine graphene band structure is preserved in the physisorbed systems but with a shift in the Dirac point away from the Fermi energy causing graphene to become n-doped in the Gr/Cu(111) system and p-doped in the Gr/Au(111) system. Chemisorption occurs in the Gr/Ni(111) system where carbon pz states mix with the nickel d states causing a gap to form at the K point, destroying the Dirac point and conical dispersion.