Predicted MF of transient galaxies as derived starting from a single Schechter function based on the data from Ilbert et al. (2013, green line), using the Peng recipe (Peng et al. 2010) for τ = 5 × 10⁷ yr (blue solid line), τ = 1 × 10⁷ yr and τ = 1 × 10⁸ yr (blue dashed lines). We compare them with the total AGN HGMF (black line) and with the HGMF computed with different luminosity cuts. In particular in the first redshift bin, cuts of log L_X> 43.8 [erg/s] (red solid line) and log L_X> 44.2 and log L_X> 43.5 [erg/s] for the lower and upper boundary, respectively, have been applied; while in the second and third redshift bins, these cuts are log L_X> 44 (brown solid line) and log L_X> 44.5 [erg/s] and log L_X> 43.5 [erg/s] for the lower and upper boundaries.