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3. A graph of a function g(x) is shown below. It is a transformation of f(x)=2¹. 10- 3 2 +- -44 +++ -2- -3+ --4- a. State in words the transformations necessary to obtain the graph shown from the graph of f(x)=2*. Use words like shift, stretch, compress, reflect, horizontal, vertical, left, right. b. Write an equation for the function g(x). g(x) 9+ 8- 74 6+

3. A graph of a function g(x) is shown below. It is a transformation of f(x)=2¹. 10- 3 2 +- -44 +++ -2- -3+ --4- a. State in words the transformations necessary to obtain the graph shown from the graph of f(x)=2*. Use words like shift, stretch, compress, reflect, horizontal, vertical, left, right. b. Write an equation for the function g(x). g(x) 9+ 8- 74 6+

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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### Transformations of Exponential Functions **Problem 3** A graph of a function \( g(x) \) is shown below. It is a transformation of \( f(x) = 2^x \). ![Graph](https://via.placeholder.com/400) In the graph, the function \( g(x) \) is plotted. The vertical \( y \)-axis ranges from \(-5\) to \(10\), and the horizontal \( x \)-axis ranges from \(-5\) to \(8\). #### a. State in words the transformations necessary to obtain the graph shown from the graph of \( f(x) = 2^x \). Use words like shift, stretch, compress, reflect, horizontal, vertical, left, right. #### b. Write an equation for the function \( g(x) \). --- ### Explanation: **Graph Explanation:** The graph represents an exponential function. The blue curve of \( g(x) \) starts from the upper left quadrant, decreasing as it moves toward the right, and approaches the \( x \)-axis without crossing it, indicating an exponential decay. This suggests that the graph of \( g(x) \) is related to the graph of \( f(x) = 2^x \), but it involves transformations such as reflection, shifts, or compressions/stretching. --- For more insights and lessons on function transformations, visit our [Educational Resources](#) page.
Transcribed Image Text:### Transformations of Exponential Functions **Problem 3** A graph of a function \( g(x) \) is shown below. It is a transformation of \( f(x) = 2^x \). ![Graph](https://via.placeholder.com/400) In the graph, the function \( g(x) \) is plotted. The vertical \( y \)-axis ranges from \(-5\) to \(10\), and the horizontal \( x \)-axis ranges from \(-5\) to \(8\). #### a. State in words the transformations necessary to obtain the graph shown from the graph of \( f(x) = 2^x \). Use words like shift, stretch, compress, reflect, horizontal, vertical, left, right. #### b. Write an equation for the function \( g(x) \). --- ### Explanation: **Graph Explanation:** The graph represents an exponential function. The blue curve of \( g(x) \) starts from the upper left quadrant, decreasing as it moves toward the right, and approaches the \( x \)-axis without crossing it, indicating an exponential decay. This suggests that the graph of \( g(x) \) is related to the graph of \( f(x) = 2^x \), but it involves transformations such as reflection, shifts, or compressions/stretching. --- For more insights and lessons on function transformations, visit our [Educational Resources](#) page.
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