The electron-energy distribution of inverse-photoemission yield at fixed photon energy is calculated for a one-dimensional model of the potential energy that allows for both a bulk band gap and a surface barrier with an image-potential tail. By varying the width of the band gap in this model, surface states can be transformed into surface resonances. The variations of peak locations, strengths, and widths during such transformations are examined in detail and compared with the predictions of simpler models.