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. Horizontal translation 5 units right ● Vertical translation 3 units up ● Reflection over the x-axis . Vertical compression by a scale facto

. Horizontal translation 5 units right ● Vertical translation 3 units up ● Reflection over the x-axis . Vertical compression by a scale facto

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Mathematics Problem Set** **Transformations of Exponential Functions** The function \( f(x) = e^{-x} \) undergoes the following transformations to create a new function: - Horizontal translation 5 units right - Vertical translation 3 units up - Reflection over the x-axis - Vertical compression by a scale factor of \(\frac{1}{2}\) Which function is a representation of the transformed function? A. \( g(x) = e^{-(x-5)} - 3 \) B. \( g(x) = -2e^{-(x-5)} - 3 \) C. \( g(x) = \frac{1}{2} e^{-x-5} + 3 \) D. \( g(x) = -\frac{1}{2} e^{-(x-5)} + 3 \) Please select the correct function from the options above to represent the transformations applied to \( f(x) \).
Transcribed Image Text:**Mathematics Problem Set** **Transformations of Exponential Functions** The function \( f(x) = e^{-x} \) undergoes the following transformations to create a new function: - Horizontal translation 5 units right - Vertical translation 3 units up - Reflection over the x-axis - Vertical compression by a scale factor of \(\frac{1}{2}\) Which function is a representation of the transformed function? A. \( g(x) = e^{-(x-5)} - 3 \) B. \( g(x) = -2e^{-(x-5)} - 3 \) C. \( g(x) = \frac{1}{2} e^{-x-5} + 3 \) D. \( g(x) = -\frac{1}{2} e^{-(x-5)} + 3 \) Please select the correct function from the options above to represent the transformations applied to \( f(x) \).
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