To investigate the effect of feedback from active galactic nuclei (AGN) on their surrounding medium, we study the diffuse X-ray emission from galaxy groups and clusters by coupling the Astrophysical Plasma Emission Code (APEC) with the cosmological hydrodynamic simulation involving AGN feedback. We construct a statistical sample of synthetic Chandra X-ray photon maps to observationally characterize the effect of AGN on the ambient medium. We show that AGN are effective in displacing the hot X-ray emitting gas from the centers of groups and clusters, and that these signatures remain evident in observations of the X-ray surface brightness profiles.