Broken-Line Functions with Unbroken Domains

Abstract

Although we no longer doubt the legitimacy of split domains as a function, students still have difficulty perceiving a graph having a shape like that of Euler and d'Alembert's string as the graph of a single function rather than of several joined functions (Vinner 1989). Given the centrality of the function concept in the school curriculum (NCTM 1989; Amit and Koren 1993), one cannot underestimate the importance of exposing students to this type of function. A method of introducing students to this concept while furnishing the teacher with material that has its own intrinsic interest (Satianov 1995).