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In this talk we will consider the finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric, compact, Kähler manifolds. Firstly we will see that we can associate each qpsh function φ on (X,ω) with a convex function F_φ in R^n and another convex function G_φ (which happens to be the Legendre transform of F_φ) on the associated Delzant polytope P. Then for the rest of the talk, we are going to show how the growth and singularity behaviour of one of these components affects the behaviour of the other two in their respective domains. This is a joint work with Dan Coman (SU), Vincent Guedj (IMT) and Ahmed Zeriahi (IMT).