  Motivated by UV realisations of Starobinsky-like inflation models, we study
generic exponential plateau-like potentials to understand whether an exact
$f(R)$-formulation may still be obtained when the asymptotic shift-symmetry of
the potential is broken for larger field values. Potentials which break the
shift symmetry with rising exponentials at large field values only allow for
corresponding $f(R)$-descriptions with a leading order term $R^{n}$ with
$1<n<2$, regardless of whether the duality is exact or approximate. The
$R^2$-term survives as part of a series expansion of the function $f(R)$ and
thus cannot maintain a plateau for all field values. We further find a lean and
instructive way to obtain a function $f(R)$ describing $m^2\phi^2$-inflation
which breaks the shift symmetry with a monomial, and corresponds to effectively
logarithmic corrections to an $R+R^2$ model. These examples emphasise that
higher order terms in $f(R)$-theory may not be neglected if they are present at
all. Additionally, we relate the function $f(R)$ corresponding to chaotic
inflation to a more general Jordan frame set-up. In addition, we consider
$f(R)$-duals of two given UV examples, both from supergravity and string
theory. Finally, we outline the CMB phenomenology of these models which show
effects of power suppression at low-$\ell$.
