In order for an autonomous agent to behave robustly in a variety of environments, it must have the ability to learn approximations to many different functions. The function approximator used by such an agent is subject to a number of constraints that may not apply in a traditional supervised learning setting. Many different function approximators exist and are appropriate for different problems. This paper proposes a set of criteria for function approximators for autonomous agents. Additionally, for those problems on which polynomial regression is a candidate technique, the paper presents an enhancement that meets these criteria. In particular, using polynomial regression typically requires a manual choice of the polynomial?s degree, trading off between function accuracy and computational and memory efficiency. Polynomial Regression with Automated Degree (PRAD) is a novel function approximation method that uses training data to automatically identify an appropriate degree for the polynomial. PRAD is fully implemented. Empirical tests demonstrate its ability to efficiently and accurately approximate both a wide variety of synthetic functions and real-world data gathered by a mobile robot.