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Exploring students' approaches to function composition from graphs
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DOI：10.1080/0020739X.2025.2572379.png)
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Abstract
En 中文
Students learn about function composition, $ ({g \circ f} )(x ) $ (g degrees f)(x), in secondary school often with a focus on composing two given equations. But what about when functions are given as graphs? This study aims to explore how students were able to reason graphically 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 students' development of deep - and diverse - meanings for composing functions.
Keywords:
Function
function composition
graphical reasoning
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