Using quantum chemical approximations to understand and predict complex transition metal chemistry, such as catalytic processes and materials properties, is an important activity in modern computational chemistry. High-level theory can sometimes provide high-precision benchmarks for systems containing transition metals, and these benchmarks can be used to understand the reliability of less expensive quantum chemical approximations that are applicable to complex systems. Here, we studied the ionization potential energy of Fe and FeC and the bond dissociation energies of FeC and FeC+ by 15 density functional approximations: M05, M06, M06-L, omega B97, omega B97X, omega B97X-D, tau-HCTHhyb, BLYP, B3LYP, M08-HX, M08-SO, SOGGA11, SOGGA11-X, M11, and M11-L. All of the functionals predict the correct spin state as the ground state of neutral iron atom, but five of them predict the wrong spin state for Fe. In the final analysis, four functionals, namely M11-L, tau-HCTHhyb, SOGGA11, and M06-L, have small mean unsigned errors when averaged over two bond dissociation energies and two ionization potentials. In fact, the results show that M11-L gives the smallest averaged mean unsigned error, i.e., M11-L is the most reliable density functional for these iron carbide systems among those studied.