A Study on the Horizontal Transformations of Elementary Functions

Yuang-Tswong Lue 
(Department of Mechanical Engineering, Taipei Chengshih University of Science and Technology, Taiwan)

Abstract: This study was designed to investigate students’ performances on the horizontal transformations between 2 of the 4 common representations, including algebraic expression (E), table (T), graph (G), and arrow diagram (D), of 6 kinds of elementary function. There were 4 booklets of test items designed for testing. The questions in each booklet were designed as the same representation. In all, there were 30 functions in a booklet.
    Transforming the graph to other 3 representations appeared to be the easiest task and transforming the algebraic expression to other 3 representations appeared to be the most difficult task. On the other hand, it was the easiest task if the target representation is arrow diagram. However, it was the most difficult task if the target representation is algebraic expression. Comparing 6 kinds of elementary function, including constant function (c), linear function (l), quadratic function (q), absolute function (a), rational function (r), and irrational function (i), we find that the difficulty level of the students’ transforming their representations was of clqari style from the easiest to the most difficult. Comparing 5 types of domain, including the finite set (F), the set of natural numbers and three integers (N’ = N∪{0,-1,-2}), the set of integers (Z), the set of rational numbers (Q), and the set of real numbers (R), we find that the difficulty level of the students’ doing horizontal transformations was generally of FZN’QR style from the easiest to the most difficult. Students also had some difficulties in doing horizontal transformation tasks.

Key words: elementary functions, domain, common representations, horizontal transformation