RUME 25
2023
Omaha, Nebraska
Exploring Geometric Reasoning with Function Composition
Page: 145
Students learn about function composition, (π β π)(π₯), in secondary school. From two given equations, one might identify the composite function algebraically via substitution, π(π(π₯)). But what about when functions are given as graphs? This study aims to explore how students were able to reason geometrically about composing functions. We identify common types of resultant graphs participants generated in trying to sketch the composition of various graphically- depicted functions, and the common types of reasoning we infer those participants engaged in while doing so. The results generate both questions, and hypotheses, about how best to support studentsβ development of deep β and diverse β meanings for composing functions.