ALFALFA measurement of the width and rotational velocity functions. Top panel: data points represent the velocity width function (WF) of galaxies measured by ALFALFA, for galaxies with . The errorbars represent the 1σ counting noise (see Eq. (A.1)), and do not include any systematic uncertainties. The dotted line is a modified Schechter fit to the data (Eq. (1)), with parameters: , log (W_∗) = 2.52 ± 0.076 km s^-1, α = −0.45 ± 0.24 and β = 2.39 ± 0.50. Bottom panel: data points represent the rotational velocity function (VF) of galaxies measured by ALFALFA, again for galaxies with . Rotational velocities, V_rot, have been obtained from inclination-corrected velocity widths according to Eq. (2). Errorbars again represent the 1σ counting noise, and do not include any systematic uncertainties. The dotted line is a modified Schechter fit to the data, with parameters: , log (V_∗) = 2.04 ± 0.18 km s^-1, α = 0.14 ± 0.41 and β = 1.46 ± 0.37.