The triggered photon structure function at center-of-mass energy 21 GeV is measured from the interaction γp → jets. Descriptions of the experimental apparatuses are given and the physics goals of the experiment are discussed. The methods used to calculate the photon structure function x\sbγ are discussed in detail, with particular attention given to Monte Carlo simulation. The energy of the photon beam is carefully analyzed and methods of understanding and compensating for multiple bremsstrahlung photons, among other beam effects, are determined. Results from experimental data are compared with theoretical predictions from both leading-order and next-to-leading-order calculations and with the results of another experiment. Some examination of other targets and other beam energies is made. We observe substantial disagreement between data and lowest order Monte Carlo. Experimental results are more consistent with NLO calculations. No experimental separation of direct and resolved photons is observed or predicted by calculation.