Inferentialism has emerged as a valuable theoretical resource in mathematics education. As a theory of meaning about the use and content of concepts, it offers a fresh perspective on traditional epistemological and linguistic questions in the field. Despite its emergence, important inferentialist ideas still need to be operationalized. In this paper, I operationalize multiple inferentialist concepts to analyze prospective secondary mathematics teachers' learning about graphs and quantitative and covariational reasoning in a mathematics content course. I use Robert Brandom's ideas about upstream, downstream, and incompatible inferences to illustrate the inferentialist mastering metaphor for learning and Brandom's ideas about objectivity. My analysis shows (a) inferentialism's capacity to address epistemological issues like objectivity and conceptual understanding, (b) the importance of attending to different types of inferences to assess learning from an inferentialist perspective, and (c) how the development of mastery is associated with virtues. I conclude by identifying the study's potential limitations and trajectories for future research.