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Activity 4.2 Comparing Exponential and Linear Functions Overview: The activity gives student data for three functions and asks them to sketch the scatter plots, calculate the ratios of successive terms for each, discuss the characteristics of the graphs of each function, identify which could be linear and which could be exponential, and to find a function for each function. Estimated Time Required: The activity should take approximately 20 minutes. Technology: None Prerequisite Concepts: How to determine when a function is linear How to determine when a function is exponential Finding formulas for exponential functions Discussion: Students often recognize that some data would not be well described by a linear function. Remind students that the defining characteristic of a linear function is that the slope is always constant no matter which two points are used for the calculation and the defining characteristic of an exponential function is that ratios between successive terms is constant. Activity 4.2 Comparing Exponential and Linear Functions x f(x) g(x) h(x) -2 0.43982 1.02711 0.95338 -1 1.31947 1.13609 1.88152 0 2.19912 1.25663 2.72743 1 3.07877 1.38996 3.47375 2 3.95842 1.53743 4.02713 a.) Make a scatter plot of the data for each of the functions above. Label graphs well. b.) Calculate the ratios of successive terms for each of the functions above. c.) Discuss characteristics of the graphs of each function, such as domain, range, asymptotes (if any), increasing vs. decreasing. d.) Which of the functions above could be linear, and which could be exponential? e.) Using 2 points of each function, derive the formulas for the functions.