  Simulations of cold dark matter make robust predictions about the slope and
normalization of the dark matter halo and subhalo mass functions on small
scales. Recent observational advances utilizing strong gravitational lensing
have demonstrated the ability of this technique to place constraints on these
quantities on subgalactic scales corresponding to dark matter halo masses of
$10^6$--$10^9\mathrm{M}_\odot$. On these scales the physics of baryons, which
make up around 17% of the matter content of the Universe but which are not
included in pure dark matter N-body simulations, are expected to affect the
growth of structure and the collapse of dark matter halos. In this work we
develop a semi-analytic model to predict the amplitude and slope of the dark
matter halo and subhalo mass functions on subgalactic scales in the presence of
baryons. We find that the halo mass function is suppressed by up to 25%, and
the slope is modified, ranging from $-1.916$ to $-1.868$ in this mass range.
These results are consistent with current measurements, but differ sufficiently
from the expectations for a dark matter only universe that it may be testable
in the near future.
