What are the limitations of computer plotting?
My attempt: a function is said $\epsilon-$plottable if every point of its graph falls within a radius $\epsilon$ of some $(\hat x_i,\hat y_i)$, where $\hat x_i$ and $\hat y_i$ are numbers that admit a finite representation (such as, but not necessarily, floating-point), and no $(\hat x_i,\hat y_i)$ has an empty $\epsilon-$neighborhoohd.
This definition is not satisfactory, as it does not account for the fact that $\hat x,\hat y$ should be related by an equation similar to $y=f(x)$. But numerically, we don't have access to $f(x)$, and not even $f(\hat x)$.
Also, if $\epsilon$ exceeds the numerical resolution, by this definition any function is plottable.
See these papers and the references therein:
Honest plotting, global extrema, and interval arithmetic, by Richard Fateman
From honest to intelligent plotting by Ron Avitzur et al
Efficient plotting the functions with discontinuities based on combined sampling, by Tomáš Bayer
Reliable two-dimensional graphing methods for mathematical formulae with two free variables, by Jeff Tupper