Integrated XLFs from Eqs. (1), (3), and (11) normalized by their respective scaling (SFR and M_*). The dash-dot-dotted line is the XLFs of the L21 model, for log[O/H]+12 = 7.2, and the dotted line for log[O/H]+12 = 9.2. Colored lines are average XLFs obtained from the luminosity sampling in PHOX: from M12b in dashed blue, L21 in dash-dotted orange, and Z12 in solid green. Corresponding lines share the same line style. The gray vertical line at log L ∼ 37 marks the maximum luminosity of a source emitting one single photon with an average energy of 0.5–8 keV.