QSO Luminosity function at various redshift intervals. Note it is NOT a Schechter function, but a double power law. [FIgure from Kembhavi & Narlikar's AGN book]
Analytic fits to the data on the left, with extrapolation to zero redshift (dotted line) comparing well with the Seyfert LF. [Figure from Peterson's AGN book].
Recasting the LF's above as an evolving space density for QSOs above a given luminosity. Note the "quasar epoch" early in cosmic history, followed by a steady decline to today's Universe with five-dex fewer per unit volume [Figure from Peterson's AGN book.]