Function offloading is a promising solution to address limitations concerning computational capacity and available energy of Connected Automated Vehicles~(CAVs) or other autonomous robots by distributing computational tasks between local and remote computing devices in form of distributed services. This paper presents a generic function offloading framework that can be used to offload an arbitrary set of computational tasks with a focus on autonomous driving. To provide flexibility, the function offloading framework is designed to incorporate different offloading decision making algorithms and quality of service~(QoS) requirements that can be adjusted to different scenarios or the objectives of the CAVs. With a focus on the applicability, we propose an efficient location-based approach, where the decision whether tasks are processed locally or remotely depends on the location of the CAV. We apply the proposed framework on the use case of service-oriented trajectory planning, where we offload the trajectory planning task of CAVs to a Multi-Access Edge Computing~(MEC) server. The evaluation is conducted in both simulation and real-world application. It demonstrates the potential of the function offloading framework to guarantee the QoS for trajectory planning while improving the computational efficiency of the CAVs. Moreover, the simulation results also show the adaptability of the framework to diverse scenarios involving simultaneous offloading requests from multiple CAVs.