In addi-tion, we found that student

In addi-tion, we found that students who described inverses as reflections were often not able to say what they should reflect in and gave a variety of pos-sibilities such as reflection in the axes or reflection in the origin. Similar results were found by Attorps et al. (2013); the students in their study were also unclear about the axis of reflection. We think that more work should be done on the link between students’ conceptions of functions and those of inverses. For example, the students who reflected the graph in task I(b) and said that the function had an inverse did not notice that the curve that they drew did not pass the vertical line test. This gives us information about their understanding of graphs of functions, and it may be that this kind of situation is the first meaningful time when students have to appreciate the full definition of function