Graphs of continuous functions and packing dimension

We prove that for a typical continuous function f∈C(X)f∈C(X) over an uncountable compact metric space X, the packing dimension of its graphGf={(x,f(x))|x∈X} is dimP⁡(X)+1dimP⁡(X)+1; we also consider decompositions of functions in C([0,1])C([0,1]) in terms of upper box dimension as well as packing dimension, which are quite different from the case of Hausdorff dimension.