  We present the first phase in our ongoing work to use Sloan Digital Sky
Survey (SDSS) data to create separate white dwarf (WD) luminosity functions for
two or more different mass ranges. In this paper, we determine the completeness
of the SDSS spectroscopic white dwarf sample by comparing a proper-motion
selected sample of WDs from SDSS imaging data with a large catalog of
spectroscopically determined WDs. We derive a selection probability as a
function of a single color (g-i) and apparent magnitude (g) that covers the
range -1.0 < g-i < 0.2 and 15 < g < 19.5. We address the observed upturn in log
g for white dwarfs with Teff <~ 12,000K and offer arguments that the problem is
limited to the line profiles and is not present in the continuum. We offer an
empirical method of removing the upturn, recovering a reasonable mass function
for white dwarfs with Teff < 12,000K. Finally, we present a white dwarf
luminosity function with nearly an order of magnitude (3,358) more
spectroscopically confirmed white dwarfs than any previous work.
