  We show that a free vector lattice over a real vector space $V$ can be
realised canonically as a vector lattice of real-valued positively homogeneous
functions on any linear subspace of its dual space that separates the points of
$V$. This is used to give intuition for the known fact that the free Banach
lattice over a Banach space $E$ can be realised as a Banach lattice of
positively homogeneous functions on $E^\ast$. It is also applied to improve the
well-known result that free vector lattices over non-empty sets can be realised
as vector lattices of real-valued functions. For infinite sets, the underlying
spaces for such realisations can be chosen to be smaller than the usual ones.
