  In this report, we consider extended real-valued functions on some real
vector space. Gerstewitz functionals are used to construct all translative
functions. We derive formulas for translative functions which are lower
semicontinuous, continuous or have sublevel sets that are given by linear
inequalities. Each extended real-valued function is shown to be the restriction
of some translative function to a hyperspace. Continuity of an arbitrary
extended real-valued function is characterized by its epigraph. Moreover, we
study the directional closedness of sets as a base for the presented results.
