Function is a multifaceted and essential concept in mathematics that includes various complex ideas such as mapping, relations between variables, algebra, input-output, and rule. Pre-service mathematics teachers' (PMTs) should have a rich understanding of these ideas for their future teaching practices. However, research showed that PMTs had a limited and superficial understanding of function as students do. Thus, a learning module was designed for improving PMTs' conceptualizations of function ideas as they relate to their personal concept definitions and examples of functions. A design-based research study was conducted with 17 senior PMTs. The study results suggest an improvement in the way PMTs define functions and identify a variety of function ideas in definitions and examples. Even if the mapping idea became dominant among all ideas in PMTs' personal concept definitions and examples, they could identify the implicit function ideas and develop an understanding of connections between ideas. We also provide suggestions for the second cycle of the intervention.