The exchange-correlation energy Exc
is a significant part of the total energy of the quasi-two-dimensional electron gas. We investigate the performance of three-dimensional density functionals Exc
[n
] in this system, showing how the local density approximation (LDA), the generalized gradient approximation (GGA), and the meta-GGA behave as functions of quantum well width or layer thickness. Shrinking the width in one direction is an example of non-uniform density scaling; we generalize the non-uniform scaling condition on the exact Exc
[n
] to densities n
(r
) that are infinitely extended. We find that, although all three semi-local approximations break down as the true two-dimensional (zero-width) limit is approached (and as the reduced density gradients diverge almost everywhere), these approximations yield good results for wide quasi-two-dimensional systems. The simple liquid drop model provides unexpectedly accurate results for exchange-correlation energies of the quasi-two-dimensional electron gas, and an insight into the domain of validity of the standard functionals. An exact-exchange functional provides the correct approach to the true two-dimensional limit.