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Several thousand core-collapse supernovae (CCSNe) of different flavors havebeen discovered so far. However, identifying their progenitors has remained anoutstanding open question in astrophysics. Studies of SN host galaxies haveproven to be powerful in providing constraints on the progenitor populations.In this paper, we present all CCSNe detected between 2009 and 2017 by thePalomar Transient Factory. This sample includes 888 SNe of 12 distinct classesout to redshift $z\approx1$. We present the photometric properties of theirhost galaxies from the far-ultraviolet to the mid-infrared and model thehost-galaxy spectral energy distributions to derive physical properties. Thegalaxy mass functions of Type Ic, Ib, IIb, II, and IIn SNe ranges from $10^{5}$to $10^{11.5}~M_\odot$, probing the entire mass range of star-forming galaxiesdown to the least-massive star-forming galaxies known. Moreover, the galaxymass distributions are consistent with models of star-formation-weighted massfunctions. Regular CCSNe are hence direct tracers of star formation. Small butnotable differences exist between some of the SN classes. Type Ib/c SNe prefergalaxies with slightly higher masses (i.e., higher metallicities) andstar-formation rates than Type IIb and II SNe. These differences are lesspronounced than previously thought. H-poor SLSNe and SNe~Ic-BL are scarce ingalaxies above $10^{10}~M_\odot$. Their progenitors require environments withmetallicities of $<0.4$ and $<1$ solar, respectively. In addition, the hosts ofH-poor SLSNe are dominated by a younger stellar population than all otherclasses of CCSNe. Our findings corroborate the notion that low-metallicity\textit{and} young age play an important role in the formation of SLSNprogenitors.

The Palomar Transient Factory Core-Collapse Supernova Host-Galaxy Sample. I. Host-Galaxy Distribution Functions and Environment-Dependence of CCSNe