The NASA/ASI imaging x-ray polarimetry explorer, which will be launched in 2021, will be the first instrument to perform spatially resolved x-ray polarimetry on several astronomical sources in the 2- to 8-keV energy band. These measurements are made possible owing to the use of a gas pixel detector (GPD) at the focus of three x-ray telescopes. The GPD allows simultaneous measurements of the interaction point, energy, arrival time, and polarization angle of detected x-ray photons. The increase in sensitivity, achieved 40 years ago, for imaging and spectroscopy with the Einstein satellite will thus be extended to x-ray polarimetry for the first time. The characteristics of gas multiplication detectors are subject to changes over time. Because the GPD is a novel instrument, it is particularly important to verify its performance and stability during its mission lifetime. For this purpose, the spacecraft hosts a filter and calibration set (FCS), which includes both polarized and unpolarized calibration sources for performing in-flight calibration of the instruments. We present the design of the flight models of the FCS and the first measurements obtained using silicon drift detectors and charge-coupled device cameras, as well as those obtained in thermal vacuum with the flight units of the GPD. We show that the calibration sources successfully assess and verify the functionality of the GPD and validate its scientific results in orbit; this improves our knowledge of the behavior of these detectors in x-ray polarimetry.