In this work, we present galaxy stellar and baryonic (stars plus cold gas) mass functions (SMF and BMF) and their halo mass dependence for two volume-limited data sets. The first, RESOLVE-B, coincides with the Stripe 82 footprint and is extremely complete down to baryonic mass Mbary ~ 10^9.1 Msun, probing the gas-rich dwarf regime below Mbary ~ 10^10 Msun. The second, ECO, covers a ~40 times larger volume (containing RESOLVE-A) and is complete to Mbary ~ 10^9.4 Msun. To construct the SMF and BMF we implement a new cross-bin sampling technique with Monte Carlo sampling from the full likelihood distributions of stellar or baryonic mass. Our SMFs exhibit the plateau feature starting below Mstar ~ 10^10 Msun that has been described in prior work. However, the BMF fills in this feature and rises as a straight power law below ~10^10 Msun, as gas-dominated galaxies become the majority of the population. Nonetheless, the low-mass slope of the BMF is not as steep as that of the theoretical dark matter halo MF. Moreover, we assign group halo masses by abundance matching, finding that the SMF and BMF separated into four physically motivated halo mass regimes reveal complex structure underlying the simple shape of the overall MFs. In particular, the satellite MFs are depressed below the central galaxy MF humps in groups with mass <10^13.5 Msun yet rise steeply in clusters. Our results suggest that satellite destruction and/or stripping are active from the point of nascent group formation. We show that the key role of groups in shaping MFs enables reconstruction of a given surveys SMF or BMF based on its group halo mass distribution.
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