Suppose a function of N real source variables X_1^N = (X_1, X_2, ..., X_N)is desired at a destination constrained to receive a limited number of bits.If the result of evaluating the function, Y = G(X_1^N), can be itselfencoded, this is the optimal strategy--the origin of Y becomes irrelevantto the communication problem.??We consider two alternative scenarios:distributed quantization, in which each X_i must be separately encoded;and linear transform coding of X_1^N.??Optimal fixed- and variable-ratescalar quantizers are derived under the conventional assumptions ofhigh-resolution quantization theory, and we find optimal transforms fortransform coding.??For certain classes of functions, examples demonstratelarge improvements over using quantizers designed to minimize distortionof the X_i's.