The X-ray afterglows (AGs) of gamma-ray bursts (GRBs) and X-ray flashes (XRFs) have, after the fast-decline phase of their prompt emission, a temporal behavior varying between two extremes. A large fraction of these AGs has a canonical light curve which, after an initial shallow-decay plateau phase, breaks smoothly into a fast power-law decline. Very energetic GRBs, contrariwise, appear to not have a break: their AGs decline like a power law from the start of the observations. Breaks and "missing breaks" are intimately related to the geometry and deceleration of the jets responsible for GRBs. In the frame of the cannonball (CB) model of GRBs and XRFs, we analyze the cited extreme behaviors (canonical and pure power law) and intermediate cases spanning the observed range of X-ray AG shapes. We show that the entire panoply of X-ray light-curve shapes—measured with Swift and other satellites—are as anticipated in the CB model. We test the expected correlations between the AG's shape and the peak and isotropic energies of the prompt radiation, strengthening a simple conclusion of the analysis of AG shapes: in energetic GRBs the break is not truly missing, it is hidden under the tail of the prompt emission, or it occurs too early to be recorded. We also verify that the spectral index of the unabsorbed AGs and the temporal indexes of their late power-law decline differ by half a unit, as predicted.