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4-7 Transforming Exponential and Logartimic Functions Obj: To transform exponential and logarithmic functions by changing parameters. (WHY? – Psychologists can use transformations of exponential functions to describe knowledge retention rates over time – ex 5) The same transformations that we applied to quadratic, linear, and polynomial functions can be performed on exponential and logarithmic functions. See below. Ex 1. Translating Exponential Functions – Graph the function 𝑔(𝑥 ) = 2𝑥 − 4 AND name the y-intercept and asymptote (hint: Graph 𝑔(𝑥) = 2𝑥 𝑢𝑠𝑖𝑛𝑔 − 2, −1, 0, 1, 2, THEN translate the graph) Ex. 2 Stretching and Reflecting Exponential Functions Graph the following 𝑔(𝑥) = 2(3)2 Name the y-intercept and asymptote 1 ℎ(𝑥) = − (2𝑥 ) 4 Name the y-intercept and asymptote Ex 3 – Transforming Logarithmic functions Graph the following: 𝑞(𝑥) = ln(𝑥 − 4) Name the y-intercept and asymptote Ex 4. - Writing Transformed functions Write the transformed function 𝑓(𝑥 ) = 0.2𝑥 is translated 2 units to the right, compressed vertically by a factor 1 of , and reflected across the x-axis. 3