  In this paper, we show that, for any $\beta \in [1,2]$, a given strictly
positive real-valued continuous function on $[0,1]$ whose graph has upper
box-counting dimension less than or equal to $\beta $ can be decomposed as a
product of two real-valued continuous functions on $[0,1]$ whose graphs have
upper box-counting dimension equal to $\beta$. We also obtain a formula for the
upper box-counting dimension of every element of a ring of polynomials in
finite number of continuous functions on $[0,1]$ over the field $\mathbb{R}.$
