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The function g(x) is a transformation of the function f(x) = 3. The coordinate plane shows the graph of both functions. <-8 -6 -4 -2 0 ((0.1) (29) (1.3) 2 Ax)=3* (2, 0) 4 6

The function g(x) is a transformation of the function f(x) = 3. The coordinate plane shows the graph of both functions. <-8 -6 -4 -2 0 ((0.1) (29) (1.3) 2 Ax)=3* (2, 0) 4 6

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Based on your knowledge of transformations, which of the equations represents the graph of \( g(x) \)? a. \( g(x) = 3^{x-2} - 1 \) b. \( g(x) = -3^{x+2} + 1 \) c. \( g(x) = -3^{x-2} + 1 \) d. \( g(x) = 3^{x+2} - 1 \)
Transcribed Image Text:Based on your knowledge of transformations, which of the equations represents the graph of \( g(x) \)? a. \( g(x) = 3^{x-2} - 1 \) b. \( g(x) = -3^{x+2} + 1 \) c. \( g(x) = -3^{x-2} + 1 \) d. \( g(x) = 3^{x+2} - 1 \)
The function \( g(x) \) is a transformation of the function \( f(x) = 3^x \). The coordinate plane shows the graph of both functions. ### Description of the Graph: 1. **Axes and Quadrants:** - The graph displays a coordinate plane with an x-axis and y-axis intersecting at the origin (0,0). 2. **Functions:** - The graph includes two different curves representing the functions \( f(x) = 3^x \) and \( g(x) \). 3. **Color Coding:** - The graph of \( f(x) = 3^x \) is shown in maroon. - The graph of \( g(x) \) is shown in teal. 4. **Labeled Points:** - On the maroon graph (\( f(x) \)): - (0, 1) - (1, 3) - (2, 9) - On the teal graph (\( g(x) \)): - (0, 1) - (2, 0) - (3, -2) - (4, -8) 5. **Behavior:** - The maroon curve (\( f(x) = 3^x \)) shows exponential growth as it moves from left to right. - The teal curve (\( g(x) \)) shows a different behavior, potentially involving a reflection or shift, altering its path significantly from \( f(x) \). This graph effectively contrasts the original function \( f(x) = 3^x \) with its transformation in \( g(x) \), illustrating their different growth patterns and point transformations.
Transcribed Image Text:The function \( g(x) \) is a transformation of the function \( f(x) = 3^x \). The coordinate plane shows the graph of both functions. ### Description of the Graph: 1. **Axes and Quadrants:** - The graph displays a coordinate plane with an x-axis and y-axis intersecting at the origin (0,0). 2. **Functions:** - The graph includes two different curves representing the functions \( f(x) = 3^x \) and \( g(x) \). 3. **Color Coding:** - The graph of \( f(x) = 3^x \) is shown in maroon. - The graph of \( g(x) \) is shown in teal. 4. **Labeled Points:** - On the maroon graph (\( f(x) \)): - (0, 1) - (1, 3) - (2, 9) - On the teal graph (\( g(x) \)): - (0, 1) - (2, 0) - (3, -2) - (4, -8) 5. **Behavior:** - The maroon curve (\( f(x) = 3^x \)) shows exponential growth as it moves from left to right. - The teal curve (\( g(x) \)) shows a different behavior, potentially involving a reflection or shift, altering its path significantly from \( f(x) \). This graph effectively contrasts the original function \( f(x) = 3^x \) with its transformation in \( g(x) \), illustrating their different growth patterns and point transformations.
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