  We present a technique to fabricate tunnel junctions between graphene and Al
and Cu, with a Si back gate, as well as a simple theory of tunneling between a
metal and graphene. We map the differential conductance of our junctions versus
probe and back gate voltage, and observe fluctuations in the conductance that
are directly related to the graphene density of states. The conventional
strong-suppression of the conductance at the graphene Dirac point can not be
clearly demonstrated, but a more robust signature of the Dirac point is found:
the inflection in the conductance map caused by the electrostatic gating of
graphene by the tunnel probe. We present numerical simulations of our
conductance maps, confirming the measurement results. In addition, Al causes
strong n-doping of graphene, Cu causes a moderate p-doping, and in high
resistance junctions, phonon resonances are observed, as in STM studies.
