  We study the process of associated photon and jet production, p+pbar -->
photon + jet + X, using 8.7 fb^-1 of integrated luminosity collected by the D0
detector at the Fermilab Tevatron Collider at a center-of-mass energy
sqrt{s}=1.96 TeV. Photons are reconstructed with rapidity |y^gamma| <1.0 or
1.5<|y^{gamma}| < 2.5 and transverse momentum pT^gamma GeV. The highest-p_T jet
is required to be in one of four rapidity regions up to |y^{jet}|< 3.2. For
each rapidity configuration we measure the differential cross sections in
pT_gamma separately for events with the same sign (y^{gamma} y^{jet}}>0) and
opposite sign (y^{gamma} y^{jet}<=0) of photon and jet rapidities. We compare
the measured triple differential cross sections, d^3 sigma / d pT_gamma
y^{gamma} y^{jet}, to next-to-leading order (NLO) perturbative QCD calculations
using different sets of parton distribution functions and to predictions from
the SHERPA and PYTHIA Monte Carlo event generators. The NLO calculations are
found to be in general agreement with the data, but do not describe all
kinematic regions.
