How and why are transformations of exponential function different from polynomials? What is a dilation away from the x or y axis? This activity provides a series of questions, explorations and dynamic visuals that will help students understand transformations of exponential functions, including a selection of homomorphic representations.
Exponential functions can be represented in multiple and equivalent ways (homomorphic). These different representations can confuse students, particularly as they try and apply prior learning associated with transformations of functions such as parabolas. The concepts are the same, the representations can be confusing. This activity is designed to help clarify the connections and subsequent transformations so that students are fluent with terms such as dilation towards the y axis.
About the Lesson
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Through a range of questions and explorations, students use an interactive TI-Nspire file to dynamically and interactively explore a variety of transformations for exponential functions. Visuals help show the difference between dilations away and toward the axes. Homomorphic representations are also included so that students can make connections between these different representations and the corresponding limitations.