We investigate the X-ray vs. optical scaling relations of poor groups to small clusters (sigma~100-700 km/s) identified in a cosmological hydrodynamic simulation of a Lambda-CDM universe, with cooling and star formation but no pre-heating. We find that the scaling relations between X-ray luminosity, X-ray temperature, and velocity dispersion show significant departures from the relations predicted by simple hydrostatic equilibrium models or simulations without cooling, having steeper L_X-sigma and L_X-T_X slopes and a "break" at \~200 km/s (~0.3 keV). These departures arise because the hot (X-ray emitting) gas fraction varies substantially with halo mass in this regime. Our predictions roughly agree with observations. Thus radiative cooling is a critical physical process in modeling galaxy groups, and may present an alternative to ad hoc models such as pre-heating or entropy floors for explaining X-ray group scaling relations.