Microcalorimeters have the potential to provide line shapes well described by a single Gaussian broadening term of few-eV width. This attribute makes the detectors especially well suited for x-ray astrophysics observations; however, low-level non-Gaussian broadening terms are expected and must be characterized. These terms depend on the composition of the x-ray absorber, the detailed x-ray absorption physics, the device thermalization processes, and the incident x-ray energy. Here we present the first measurements targeted at understanding the extended line-spread function (LSF) of x-ray microcalorimeter pixels under development for the X-ray Integral Field Unit on the Athena X-ray Observatory. These pixels are composed of Mo/Au transition-edge sensors with overhanging electroplated Au/Bi absorbers. We have measured the line shapes using monochromatic x-ray sources with <; 1-eV width at several x-ray energies (0.85, 0.93, 1.25, 1.5, 5.4 and 8.0 keV) across the instrument bandpass (0.3-12 keV) and have modeled the line profiles. These results are compared to the extended LSF of the Hitomi microcalorimeter pixels that used HgTe absorbers.