Hard-scattering of point-like constituents (or partons) in p-p collisions was discovered at the CERN-ISR1 in 1972 by measurements utilizing inclusive single or pairs of hadrons with large transverse momentum (pT). Due to the steeply falling power-law pT spectrum of the hard-scattered partons, the inclusive single particle (e.g. π0) pTt spectrum from parton fragmentation to a jet is dominated by trigger fragments with large zt ~ 0.7–0.8, where zt = pTt/pTjet is the fragmentation variable. It was generally assumed, following Feynman, Field and Fox,2 as shown by data from the CERN-ISR experiments, that the pTa distribution of away side hadrons from a single particle trigger [with pTt], corrected for zt, would be the same as that from a jet-trigger and follow the same fragmentation function as observed in e+e− or DIS. PHENIX3 attempted to measure the fragmentation function from the away side xE ~ PTa/pTt distribution of charged particles triggered by a π0 in p − p collisions at RHIC and showed by explicit calculation that the xE distribution is actually quite insensitive to the fragmentation function. Illustrations of the original arguments and ISR results will be presented. Then the lack of sensitivity to the fragmentation function will be explained, and an analytic formula for the xE distribution given, in terms of incomplete Gamma functions, for the case where the fragmentation function is exponential. The away-side distribution in this formulation has the nice property that it both exhibits xE scaling and is directly sensitive to the ratio of the away jet [Formula: see text] to that of the trigger jet, [Formula: see text], and thus can be used, for example, to measure the relative energy loss of the two jets from a hard-scattering which escape from the medium in A + A collisions. Comparisons of the analytical formula to RHIC measurements will be presented, including data from STAR4,5 and PHENIX,3,6 leading to some interesting conclusions.