Applying Function Transformations to Model Dynamic Systems

Abstract

Being able to transform functions due to given conditions is an essential math skill. A preliminary survey of research on teaching transformations has shown that majority of assessment items gravitated toward predicting new graphs due to assigned shifts, compressions, or reflections. Real-life applications of these concepts were rarely discussed. The activity focuses on identifying possible transformations of trajectories of projected objects and constructing new functions. STEM context was provided in the form of a physics simulation Projectile Motion that is available for free at http://phet.colorado.edu/sims/projectile-motion/projectile-motion_en.html. Parabolic trajectories were generated by varying the parameters of the object’s initial velocity and its relative position. A group (N = 25) of pre-calculus students mathematized a parent-simulated trajectory and then used it to formulate algebraic functions of other trajectories. It was hypothesized that situating the concept of function transformation in an environment that related to students’ prior experience would enhance the purpose of formulating algebraic representations and explicate on applicability of transformation. Analysis of posttest results revealed that situating the learning in realistic contexts brought another dimension to understanding function transformations and infused a deeper understanding of the techniques of constructing transformed functions.