[yorwba]

I think the polynomial is supposed to have only integer coefficients, which means that it will only take integer values at integer coordinates. Since real-valued coefficients need some rational approximation anyway, and rational coefficients can be rescaled, that assumption is easy to justify. (Alternatively, the coefficients might be in some finite field, but then the range is discrete as well.)

[weber111]

Makes sense - thanks! I was confused by the continuous plot.