We combine recent estimates of dust extinction at z ∼ 4–7 with UV luminosity function (LF) determinations to derive star formation rate (SFR) functions at z ∼ 4–7. SFR functions provide a more physical description of galaxy buildup at high redshift and allow for direct comparisons to SFRs at lower redshifts determined by a variety of techniques. Our SFR functions are derived from well-established z ∼ 4–7 UV LFs, UV-continuum slope trends with redshift and luminosity, and infrared excess (IRX)–β relations. They are well described by Schechter relations. We extend the comparison baseline for SFR functions to z ∼ 2 by considering recent determinations of the Hα and mid-IR LFs. The low-end slopes of the SFR functions are flatter than for the UV LFs, Δα ∼ +0.13, and show no clear evolution with cosmic time ( z ∼ 0–7). In addition, we find that the characteristic value SFR* from the Schechter fit to the SFR function exhibits consistent, and substantial, linear growth as a function of redshift from ∼5 M ☉ yr −1 at z ∼ 8, 650 Myr after the big bang, to ∼100 M ☉ yr −1 at z ∼ 2, ∼2.5 Gyr later. Recent results at z ∼ 10, close to the onset of galaxy formation, are consistent with this trend. The uniformity of this evolution is even greater than seen in the UV LF over the redshift range z ∼ 2–8, providing validation for our dust corrections. These results provide strong evidence that galaxies build up uniformly over the first 3 Gyr of cosmic time.
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