Steep functions in astronomy: the RQSO z-cutoff debate

Astronomers traditionally find steep, open-ended functions difficult: the log N - log S curve for example, or the probability-area-radius relation in making cross-waveband identifications. The debate over the existence of a redshift cutoff for RQSOs (radio-loud QSOs; Jarvis and Rawlings 2000, Wall et al. 2005) is a case in point: an instance in which a second-order effect involving radio-variable QSOs, initially selected by survey from a population with a steep source count, leads to discrepant results from different analyses. A redshift cutoff is present in optically-selected QSOs of the SDSS and in X-ray selected QSOs of XMM, ROSAT and CHANDRA. A similar cutoff for radio-loud QSOs is important to establish, because if present, no known type of obscuration can be responsible. Such a space-density diminution then defines an epoch of creation for galaxy hosts of massive black holes powering AGN, a datum for galaxy formation. I discuss the resolution of the debate: the issue is highly relevant to modern surveys and their follow-up observations.