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y=-ex+¹+3 Domain: Range: . Asymptote: End Behavior: Original Function: Describe Transformation: y=e Domain: Range: Asymptote: End Behavior: y = 2.In(x) Original Function: Describe Transformation:

y=-ex+¹+3 Domain: Range: . Asymptote: End Behavior: Original Function: Describe Transformation: y=e Domain: Range: Asymptote: End Behavior: y = 2.In(x) Original Function: Describe Transformation:

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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**Exponential and Logarithmic Function Analysis** The following worksheet provides a framework for analyzing two functions: an exponential function and a logarithmic function. The worksheet features graphs and spaces to fill out key characteristics of each function. --- ### Function 1: \( y = -e^{x+1} + 3 \) **Graph:** - A blank graph is provided to plot the exponential function, showing both the x-axis and y-axis which intersect at the origin. **To Analyze:** - **Domain:** __________ - **Range:** __________ - **Asymptote:** __________ - **End Behavior:** __________ - **Original Function:** __________ - **Describe Transformation:** __________ --- ### Function 2: \( y = 2 \cdot \ln(x) \) **Graph:** - A blank graph is available for the logarithmic function to be plotted, showing both the x-axis and y-axis intersecting at the origin. **To Analyze:** - **Domain:** __________ - **Range:** __________ - **Asymptote:** __________ - **End Behavior:** __________ - **Original Function:** __________ - **Describe Transformation:** __________ --- Use this worksheet as a tool to explore the properties of exponential and logarithmic functions, focusing on transformations, domains, ranges, and asymptotes.
Transcribed Image Text:**Exponential and Logarithmic Function Analysis** The following worksheet provides a framework for analyzing two functions: an exponential function and a logarithmic function. The worksheet features graphs and spaces to fill out key characteristics of each function. --- ### Function 1: \( y = -e^{x+1} + 3 \) **Graph:** - A blank graph is provided to plot the exponential function, showing both the x-axis and y-axis which intersect at the origin. **To Analyze:** - **Domain:** __________ - **Range:** __________ - **Asymptote:** __________ - **End Behavior:** __________ - **Original Function:** __________ - **Describe Transformation:** __________ --- ### Function 2: \( y = 2 \cdot \ln(x) \) **Graph:** - A blank graph is available for the logarithmic function to be plotted, showing both the x-axis and y-axis intersecting at the origin. **To Analyze:** - **Domain:** __________ - **Range:** __________ - **Asymptote:** __________ - **End Behavior:** __________ - **Original Function:** __________ - **Describe Transformation:** __________ --- Use this worksheet as a tool to explore the properties of exponential and logarithmic functions, focusing on transformations, domains, ranges, and asymptotes.
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