  The velocity function derived from large scale surveys can be compared with
the predictions of LCDM cosmology, by matching the measured rotation velocities
Vrot of galaxies to the maximum circular velocity of dark matter (DM) halos
Vmax. For Vrot<50km/s, a major discrepancy arises between the observed and LCDM
velocity functions. However, the manner in which different observational
measures of Vrot are associated with Vmax is not straight forward in dwarf
galaxies. We instead relate galaxies to DM halos using the empirical baryon-
mass to halo-mass relation, and show that different observational measures of
Vrot result in very different velocity functions. We show how the W50 velocity
function, i.e. using the HI profile line width at 50% of peak HI flux to
measure Vrot, can be reconciled with a LCDM cosmology. Our semi-empirical
methodology allows us to determine the region of rotation curves that are
probed by HI measurements (RHI), and shows that the Vrot of dwarfs are
generally measured at a fraction of Rmax, explaining their tendency to have
rising rotation curves. We provide fitting formulae for relating RHI and Reff
(the effective radius) to the virial radius of DM halos. To continue to use
velocity functions as a probe of LCDM cosmology, it is necessary to be precise
about how the different measures of rotation velocity are probing the mass of
the DM halos, dropping the assumption that any measure of rotational velocity
can be equally used as a proxy for Vmax.
