Pedagogically Inconvenient Functions for Teaching Transformations

SummaryPedagogically inconvenient functions are those that look the same under two different types of transformations. We characterize those functions that look the same under vertical and horizontal stretches. In the continuous case, this leads to an expected conclusion; in the noncontinuous case, it does not. Though the question is quite simple and accessible, a full characterization leads us in some surprising mathematical directions.