Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
### Graph Transformations #### (a) Graph of \( y = f(x) \) - **Objective:** Draw the graph of \( y = f(-x) \). - **Description:** The provided graph displays \( y = f(x) \) as a V-shaped graph. It has vertices at (-4, -2), (0, 4), and (4, -2). #### Instructions for Transformation: - Reflect the original graph over the y-axis for \( y = f(-x) \). --- #### (b) Graph of \( y = g(x) \) - **Objective:** Draw the graph of \( y = -g(x) \). - **Description:** The provided graph shows a linear function decreasing from the point (-5, 5) intersecting the x-axis at (0, 0) and continuing to (5, -5). #### Instructions for Transformation: - Reflect the original graph over the x-axis to obtain \( y = -g(x) \). ### Toolbar Icons - **Eraser:** Clear parts of the graph. - **Pen:** Draw and annotate on the graph. - **Line Tool:** Draw straight lines. - **Grid Toggle:** Show or hide the grid. - **Reset Button:** Clear all changes. - **Help Button:** Access help resources. *This content is intended for educational purposes and provides an interactive way to explore graph transformations.*
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Transcribed Image Text:### Graph Transformations #### (a) Graph of \( y = f(x) \) - **Objective:** Draw the graph of \( y = f(-x) \). - **Description:** The provided graph displays \( y = f(x) \) as a V-shaped graph. It has vertices at (-4, -2), (0, 4), and (4, -2). #### Instructions for Transformation: - Reflect the original graph over the y-axis for \( y = f(-x) \). --- #### (b) Graph of \( y = g(x) \) - **Objective:** Draw the graph of \( y = -g(x) \). - **Description:** The provided graph shows a linear function decreasing from the point (-5, 5) intersecting the x-axis at (0, 0) and continuing to (5, -5). #### Instructions for Transformation: - Reflect the original graph over the x-axis to obtain \( y = -g(x) \). ### Toolbar Icons - **Eraser:** Clear parts of the graph. - **Pen:** Draw and annotate on the graph. - **Line Tool:** Draw straight lines. - **Grid Toggle:** Show or hide the grid. - **Reset Button:** Clear all changes. - **Help Button:** Access help resources. *This content is intended for educational purposes and provides an interactive way to explore graph transformations.*
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