In this article we give, for an arbitrary continuous function which is linear on the octants of an explicit representation in terms of a max–min expression. Moreover, we also consider its representation as the difference of two sublinear functions and determine minimal representations in the sense of Pallaschke and Urbański [D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets – Fractional Arithmetic with Convex Sets, Vol. 548, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, 2002].