A discussion is given of the f-sum rule obeyed by the density response function of a bounded electron gas. Particular attention is given to approximate models for a jellium slab. We prove that RPA infinite barrier models (both classical and quantal) are perfectly consistent with the f-sum rule as well as the related dielectric sum rule. In addition, the classical infinite barrier model is shown to satisfy the surface sum rules of Inglesfield and Wikborg.