Natural selection dictates that cells constantly adapt to dynamically changing environments in a context-dependent manner. Gene-regulatory networks often mediate the cellular response to perturbation, and an understanding of cellular adaptation will require experimental approaches aimed at subjecting cells to a dynamic environment that mimics their natural habitat. Here we monitor the response of Saccharomyces cerevisiae metabolic gene regulation to periodic changes in the external carbon source by using a microfluidic platform that allows precise, dynamic control over environmental conditions. We show that the metabolic system acts as a low-pass filter that reliably responds to a slowly changing environment, while effectively ignoring fast fluctuations. The sensitive low-frequency response was significantly faster than in predictions arising from our computational modelling, and this discrepancy was resolved by the discovery that two key galactose transcripts possess half-lives that depend on the carbon source. Finally, to explore how induction characteristics affect frequency response, we compare two S. cerevisiae strains and show that they have the same frequency response despite having markedly different induction properties. This suggests that although certain characteristics of the complex networks may differ when probed in a static environment, the system has been optimized for a robust response to a dynamically changing environment.