The transition from the amplification of spontaneous emission to superfluorescence in a three-level and swept-gain medium excited by an x-ray free-electron-laser pulse is theoretically investigated. Given the specific timescale of an x-ray free-electron-laser pulse, we investigate the swept pumping process in detail, and our results show that the temporal structure of an x-ray free-electron-laser pulse plays a more critical role than its peak intensity does for producing population inversion. The typical watershed of two radiant regions depends on the optical depth of the gain medium for a given coherence time, namely, the particle number density and medium length are equally important. However, we find that medium length plays a more important role than particle density for making the forward-backward asymmetry. The transient gain length and the total medium length are identified as two important factors to observe length-induced backward transition. The present results suggest an application of parametric controls over a single-pass-amplified light source.