  Several thousand core-collapse supernovae (CCSNe) of different flavors have
been discovered so far. However, identifying their progenitors has remained an
outstanding open question in astrophysics. Studies of SN host galaxies have
proven to be powerful in providing constraints on the progenitor populations.
In this paper, we present all CCSNe detected between 2009 and 2017 by the
Palomar Transient Factory. This sample includes 888 SNe of 12 distinct classes
out to redshift $z\approx1$. We present the photometric properties of their
host galaxies from the far-ultraviolet to the mid-infrared and model the
host-galaxy spectral energy distributions to derive physical properties. The
galaxy 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 galaxies
down to the least-massive star-forming galaxies known. Moreover, the galaxy
mass distributions are consistent with models of star-formation-weighted mass
functions. Regular CCSNe are hence direct tracers of star formation. Small but
notable differences exist between some of the SN classes. Type Ib/c SNe prefer
galaxies with slightly higher masses (i.e., higher metallicities) and
star-formation rates than Type IIb and II SNe. These differences are less
pronounced than previously thought. H-poor SLSNe and SNe~Ic-BL are scarce in
galaxies above $10^{10}~M_\odot$. Their progenitors require environments with
metallicities of $<0.4$ and $<1$ solar, respectively. In addition, the hosts of
H-poor SLSNe are dominated by a younger stellar population than all other
classes of CCSNe. Our findings corroborate the notion that low-metallicity
\textit{and} young age play an important role in the formation of SLSN
progenitors.
