  Dwarf, irregular and infrared-luminous starburst galaxies are all known to
have "steep" luminosity functions with faint-end behavior roughly
phi(L)-propto- L^(-1.8). This form is exactly what is expected if the
luminosities of these objects fade with time as L-propto-t^(-1.3), because the
objects spend more time at low luminosities than high, even if they form with a
wide range of initial masses. Models of young stellar populations show this
fading behavior when the star formation has occured in a single, short, recent
burst. Steep luminosity functions therefore do not require steep mass functions
if the galaxies are powered by fading bursts. The local-galaxy H-alpha
luminosity function---which is less steep than L^(-1.8)---is also well-fit by
this mechanism, because ionizing photon flux fades much more quickly than
broad-band optical luminosity. An age-luminosity relation and a
wavelength-dependence of the luminosity function are both predicted. In the
context of this mechanism, the slope of the luminosity function provides a
constraint on the stellar initial mass function in the bursts.
