I review an analytic model that can capture the essential features of the observed quasar luminosity function using a physical model of a brief period of a rapidly growing rate of formation of direct collapse black holes (DCBHs) in the early universe. The DCBH scenario has been proposed in order to meet a key challenge to the theory of the formation of supermassive black holes (SMBHs): the observation of very massive (M > 109 Msun) and luminous (L > 1013 Lsun) quasars already in place by z ~ 7, when the age of the universe was just ~800 Myr. Working in this scenario, we show that the mass function of SMBHs after a limited time period of rapid formation and super-Eddington accretion of indivdual SMBHs, can be described as a tapered power law function. The power law at intermediate masses has an index that is the dimensionless ratio α = λ/γ, where λ is the growth rate of the number density of DCBHs during their formation era, and γ is the growth rate of DCBH masses by super-Eddington accretion during the same growth era. A second feature is a break in the power-law profile at high masses, above which the mass function declines rapidly. The location of the break is related to the dimensionless number β = γT, where T is the duration of the growth era. If the SMBHs continue to grow at later times at an Eddington-limited accretion rate, then the observed quasar luminosity function can be directly related to the tapered power-law mass function.