Given a well-behaved real function Y of a real random variable X and the first two or three moments of X, expressions are derived for the moments of Y as linear combinations of powers of the point estimates y(x(+)) and y(x(-)), where x(+) and x(-) are specific values of X. Higher-order approximations and approximations for discontinuous Y using more point estimates are also given. Second-moment approximations are generalized to the case when Y is a function of several variables.