Function Transformations

This unit is designed to familiarize students with the ideas of how various functions can be transformed, and the effect those transformations have on equations, graphs, and contextual situations. The function families were chosen to be simple enough for students to readily understand, and also sophisticated enough to clearly demonstrate the effects of dilations and translations. The skills and principles to be learned apply to virtually all function families, and will give a solid foundation for more advanced studies in functions. The approach of this unit is primarily investigative in nature – students will examine the effects various transformations have on function equations and graphs to develop conjectures and generalized understanding. To that end, the Geometry Expressions (Gx) software will be used extensively as an investigative tool and a means to check the accuracy of conjectures. Ideally, students will have previously completed the Intro to Unit Circle Trigonometry lesson using Gx, as that introduces the general learning pattern, as well as many of the software features they will be using. If they haven’t used Gx before, it is a good lesson to do as a review, prior to starting this unit.