Conceptual understanding about piecewise functions based on graphical representation

Abstract

Understanding the concept of function is very important in learning mathematics. Students’ understanding of functions can be seen from how students represent these functions with a graph. The present research aims to describe second-year mathematics students’ conceptual understanding about piecewise functions seen from the graphic images they made. The subjects were 5 second-year students of mathematics study program in Universitas Negeri Malang, Indonesia. Data collected by conducting written tests and interviews with students. Students are given one problem about drawing graphs of polynomial functions that are defined piecewise. The collected data were analysed using descriptive qualitative method. After that, interviews were conducted related to graphic images made by students. From the findings, it was found that only one student understood the concept of the piecewise function correctly. He understood that each of the three polynomials defined in the piecewise function had different domains and could graph them accurately. The remaining students defined the piecewise function by using a single algebraic formula by summing each a lgebraic formula in the given piecewise function. Misunderstanding of the concept of piecewise functions is due to their lack of understanding of the domain and the continuity of a function at certain intervals.