  Galaxies' stellar masses, gas-phase oxygen abundances (metallicity), and star
formation rates (SFRs) obey a series of empirical correlations, most notably
the mass-metallicity relation (MZR) and fundamental metallicity relation (FZR),
which relates oxygen abundance to a combination of stellar mass and SFR.
However, due to the difficulty of measuring oxygen abundances and SFRs in
galaxies that host powerful active galactic nuclei (AGN), to date it is unknown
to what extent AGN-host galaxies also follow these correlations. In this work,
we apply Bayesian methods to the MaNGA integral field spectrographic (IFS)
survey that allow us to measure oxygen abundances and SFRs in AGN hosts, and
use these measurements to explore how the MZR and FZR differ between galaxies
that do and do not host AGN. We find similar MZRs at stellar masses above
$10^{10.5} \mathrm{M}_\odot$, but that at lower stellar masses AGN hosts show
up to $\sim 0.2$ dex higher oxygen abundances. The offset in the FZR is
significantly smaller, suggesting that the larger deviation in the MZR is a
result of AGN-host galaxies having systematically lower SFRs at fixed stellar
mass. However, within the AGN-host sample there is little correlation between
SFR and oxygen abundance. These findings support a scenario in which an AGN can
halt efficient gas accretion, which drives non-AGN host galaxies to both higher
SFR and lower oxygen abundance, resulting in the galaxy evolving off the
star-forming main sequence (SFMS). As a consequence, as the SFR declines for an
individual system its metallicity remains mostly unchanged.
