Results are presented from a phenomenological analysis of recent measurements of jet suppression and modifications of jet fragmentation functions in Pb+Pb collisions at the LHC. Particular emphasis is placed on the impact of the differences between quark and gluon jet quenching on the transverse momentum ($p_{T}^{jet}$) dependence of the jet $R_{AA}$ and on the fragmentation functions, $D(z)$. Primordial quark and gluon parton distributions were obtained from PYTHIA8 and were parameterized using simple power-law functions and extensions to the power-law function which were found to better describe the PYTHIA8 parton spectra. A simple model for the quark energy loss based on the shift formalism is used to model $R_{AA}$ and $D(z)$ using both analytic results and using direct Monte-Carlo sampling of the PYTHIA parton spectra. The model is capable of describing the full $p_{T}^{jet}$ , rapidity, and centrality dependence of the measured jet $R_{AA}$ using three effective parameters. A key result from the analysis is that the $D(z)$ modifications observed in the data, excluding the enhancement at low-$z$, may result primarily from the different quenching of the quarks and gluons. The model is also capable of reproducing the charged hadron $R_{AA}$ at high transverse momentum. Predictions are made for the jet $R_{AA}$ at large rapidities where it has not yet been measured and for the rapidity dependence of $D(z)$.
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