We present the mid-infrared colors of X-ray-detected AGN and explore mid-infrared selection criteria. Using a statistical matching technique, the likelihood ratio, over 900 IRAC counterparts were identified with a new MUSYC X-ray source catalog that includes ~1000 published X-ray sources in the Chandra Deep Field-South and Extended Chandra Deep Field-South. Most X-ray-selected AGN have IRAC spectral shapes consistent with power-law slopes, f_{nu} ~ nu^{alpha}, and display a wide range of colors, -2 < alpha < 2. Although X-ray sources typically fit to redder (more negative alpha) power-laws than non-X-ray detected galaxies, more than 50% do have flat or blue (galaxy-like) spectral shapes in the observed 3-8 micron band. Only a quarter of the X-ray selected AGN detected at 24 micron are well fit by featureless red power laws in the observed 3.6-24 micron, likely the subset of our sample whose infrared spectra are dominated by emission from the central AGN region. Most IRAC color-selection criteria fail to identify the majority of X-ray-selected AGN, finding only the more luminous AGN, the majority of which have broad emission lines. In deep surveys, these color-selection criteria select 10-20% of the entire galaxy population and miss many moderate luminosity AGN.
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