A qualitative description of graphs of discontinuous polynomial functions

We prove that, if f:R^n\to R satisfies Fr\'echet's functional equation and f(x_1,...,x_n) is not an ordinary algebraic polynomial in the variables x_1,...,x_n, then f is unbounded on all non-empty open set U of R^n. Furthermore, the closure of its graph contains an unbounded open set.Comment: 9 pages, submitted to a journa