Background: Every student has the ability to think, especially the ability to think when solving mathematical problems. The teacher must explore this ability to determine student understanding of the material being taught. Functions are essential because they are the basis for understanding algebra. The way of thinking about function is called functional thinking. Objective: This study aims to investigate the functional thinking process of students in solving mathematical problems based on the APOS theory. Design: This type of research is qualitative through an exploratory, descriptive approach. Setting and participants: Two out of 44 university students that can communicate fluently when working on questions using the think-aloud and interview methods. Data analysis: Analysis of students' functional thinking processes using the triangulation method, namely comparing think-aloud data, student answer sheets, and interview results. Results: This study found two ways of student functional thinking processes, namely semi-compositional functional thinking processes and compositional functional thinking processes, where students can generalise the relationship between quantity variations in the form of a composition function. Conclusion:This study investigates the functional thinking process of students in exploring the understanding of the concept of function so that students are expected to be able to represent and generalise function forms.