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

A matter of measurement: rotation velocities and the velocity function of dwarf galaxies