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Summary:
The article focuses on students' understanding of graphs of functions. Interviews were conducted with 22 students in who solved some tasks on classifications of graphs of functions. For the analysis of data, we used the theory of prototypes and the theory of exemplification and the framework of hypothetical learning trajectories. Some extracts from the interviews are given to illustrate main results. For instance, we observed that students focus on various aspects of the graph (linearity, passing through the origin of the coordinate system, etc.) and mark them as important. As students acquire more experience with graphs of functions, they focus more on the curve of the graph and the importance of aspects changes. Nevertheless, some of them stay strong (real context of the graph) during the whole process and there are important mathematical aspects (as continuity) which are systematically underestimated.
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