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In this work, we present galaxy stellar and baryonic (stars plus cold gas)mass functions (SMF and BMF) and their halo mass dependence for twovolume-limited data sets. The first, RESOLVE-B, coincides with the Stripe 82footprint 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 toMbary ~ 10^9.4 Msun. To construct the SMF and BMF we implement a new "cross-binsampling" technique with Monte Carlo sampling from the full likelihooddistributions of stellar or baryonic mass. Our SMFs exhibit the "plateau"feature starting below Mstar ~ 10^10 Msun that has been described in priorwork. However, the BMF fills in this feature and rises as a straight power lawbelow ~10^10 Msun, as gas-dominated galaxies become the majority of thepopulation. Nonetheless, the low-mass slope of the BMF is not as steep as thatof the theoretical dark matter halo MF. Moreover, we assign group halo massesby abundance matching, finding that the SMF and BMF separated into fourphysically motivated halo mass regimes reveal complex structure underlying thesimple shape of the overall MFs. In particular, the satellite MFs are depressedbelow the central galaxy MF "humps" in groups with mass <10^13.5 Msun yet risesteeply in clusters. Our results suggest that satellite destruction and/orstripping are active from the point of nascent group formation. We show thatthe key role of groups in shaping MFs enables reconstruction of a givensurvey's SMF or BMF based on its group halo mass distribution.

RESOLVE and ECO: The Halo Mass-Dependent Shape of Galaxy Stellar and Baryonic Mass Functions