  In this paper we investigate the relation between the scaling properties of
the linear response function $R(t,s)$, of the thermoremanent magnetization
(TRM) and of the zero field cooled magnetization (ZFC) in the context of phase
ordering kinetics. We explain why the retrival of the scaling properties of
$R(t,s)$ from those of TRM and ZFC is not trivial. Preasymptotic contributions
generate a long crossover in TRM, while ZFC is affected by a dangerous
irrelevant variable. Lack of understanding of both these points has generated
some confusion in the literature. The full picture relating the exponents of
all the quantities involved is explicitely illustrated in the framework of the
large $N$ model. Following this scheme, an assessment of the present status of
numerical simulations for the Ising model can be made. We reach the conclusion
that on the basis of the data available up to now, statements on the scaling
properties of $R(t,s)$ can be made from ZFC but not from TRM. From ZFC data for
the Ising model with $d=2,3,4$ we confirm the previously found linear
dependence on dimensionality of the exponent $a$ entering $R(t,s) \sim
s^{-(1+a)}f(t/s)$. We also find evidence that a recently derived form of the
scaling function $f(x)$, using local scale invariance arguments [M.Henkel,
M.Pleimling, C.Godr\`{e}che and J.M.Luck, Phys.Rev.Lett. {\bf 87}, 265701
(2001)], does not hold for the Ising model.
