Following Zhao, Morrison, and Parr [Q. Zhao, R. C. Morrison, and R. G. Parr. Phys. Rev. A 50, 2138 (1994)], we examine the effective homogeneity of the exact exchange-correlation energy functional for a set of open-shell atoms. By explicitly considering the influence of the integer discontinuity in the exact exchange-correlation potential, our results suggest that on the limiting electron deficient and electron abundant sides of the integer, the exact functional is poorly represented by any functional that is approximately homogeneous in the electron density. In contrast, a functional whose potential averages over the exact discontinuity must be approximately homogeneous of degree 4/3 in the density, and this is particularly so for the heavier atoms. This observation supports the view that continuum functionals, dominated by local density exchange, must exhibit such an average behavior. The asymptotic breakdown of this average behavior in conventional continuum functionals has important consequences for the computation of long-range properties.