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### Problem Statement: **Determine the Coordinates of the Transformed Vertex:** Consider the graph of the absolute value function \( y = |x| \). This graph has been transformed according to the following criteria: 1. **Vertical Stretch:** The graph is stretched vertically by a factor of 3. 2. **Horizontal Shift:** The graph is shifted 2 units to the right. 3. **Vertical Shift:** The graph is shifted vertically down by 6 units. **Question:** What are the coordinates of the new vertex after these transformations? ### Answer Choices: - (2, -6) - (-2, 6) - (2, 18) - (2, 6) ### Explanation of Transformations: 1. **Vertical Stretch by a Factor of 3:** - The general effect is given by \( y = a|x| \), where \( a \) in this case is 3, modifying the equation to \( y = 3|x| \). However, this does not affect the x-coordinate of the vertex. 2. **Right Horizontal Shift of 2 Units:** - This shift moves the graph in the positive x-direction modifying the equation further to \( y = 3|x - 2| \). - The x-coordinate of the vertex moves from 0 to 2. 3. **Vertical Shift Downwards by 6 Units:** - This translates the graph downward, modifying the equation to \( y = 3|x - 2| - 6 \). - The y-coordinate of the vertex moves from 0 to -6. **Initial Vertex (Original graph of \( y = |x| \)):** - \((0, 0)\) **New Vertex:** - After applying the transformations, the new vertex is at \((2, -6)\). ### Correct Answer: - **(2, -6)**

### Problem Statement: **Determine the Coordinates of the Transformed Vertex:** Consider the graph of the absolute value function \( y = |x| \). This graph has been transformed according to the following criteria: 1. **Vertical Stretch:** The graph is stretched vertically by a factor of 3. 2. **Horizontal Shift:** The graph is shifted 2 units to the right. 3. **Vertical Shift:** The graph is shifted vertically down by 6 units. **Question:** What are the coordinates of the new vertex after these transformations? ### Answer Choices: - (2, -6) - (-2, 6) - (2, 18) - (2, 6) ### Explanation of Transformations: 1. **Vertical Stretch by a Factor of 3:** - The general effect is given by \( y = a|x| \), where \( a \) in this case is 3, modifying the equation to \( y = 3|x| \). However, this does not affect the x-coordinate of the vertex. 2. **Right Horizontal Shift of 2 Units:** - This shift moves the graph in the positive x-direction modifying the equation further to \( y = 3|x - 2| \). - The x-coordinate of the vertex moves from 0 to 2. 3. **Vertical Shift Downwards by 6 Units:** - This translates the graph downward, modifying the equation to \( y = 3|x - 2| - 6 \). - The y-coordinate of the vertex moves from 0 to -6. **Initial Vertex (Original graph of \( y = |x| \)):** - \((0, 0)\) **New Vertex:** - After applying the transformations, the new vertex is at \((2, -6)\). ### Correct Answer: - **(2, -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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### Problem Statement: **Determine the Coordinates of the Transformed Vertex:** Consider the graph of the absolute value function \( y = |x| \). This graph has been transformed according to the following criteria: 1. **Vertical Stretch:** The graph is stretched vertically by a factor of 3. 2. **Horizontal Shift:** The graph is shifted 2 units to the right. 3. **Vertical Shift:** The graph is shifted vertically down by 6 units. **Question:** What are the coordinates of the new vertex after these transformations? ### Answer Choices: - (2, -6) - (-2, 6) - (2, 18) - (2, 6) ### Explanation of Transformations: 1. **Vertical Stretch by a Factor of 3:** - The general effect is given by \( y = a|x| \), where \( a \) in this case is 3, modifying the equation to \( y = 3|x| \). However, this does not affect the x-coordinate of the vertex. 2. **Right Horizontal Shift of 2 Units:** - This shift moves the graph in the positive x-direction modifying the equation further to \( y = 3|x - 2| \). - The x-coordinate of the vertex moves from 0 to 2. 3. **Vertical Shift Downwards by 6 Units:** - This translates the graph downward, modifying the equation to \( y = 3|x - 2| - 6 \). - The y-coordinate of the vertex moves from 0 to -6. **Initial Vertex (Original graph of \( y = |x| \)):** - \((0, 0)\) **New Vertex:** - After applying the transformations, the new vertex is at \((2, -6)\). ### Correct Answer: - **(2, -6)**
Transcribed Image Text:### Problem Statement: **Determine the Coordinates of the Transformed Vertex:** Consider the graph of the absolute value function \( y = |x| \). This graph has been transformed according to the following criteria: 1. **Vertical Stretch:** The graph is stretched vertically by a factor of 3. 2. **Horizontal Shift:** The graph is shifted 2 units to the right. 3. **Vertical Shift:** The graph is shifted vertically down by 6 units. **Question:** What are the coordinates of the new vertex after these transformations? ### Answer Choices: - (2, -6) - (-2, 6) - (2, 18) - (2, 6) ### Explanation of Transformations: 1. **Vertical Stretch by a Factor of 3:** - The general effect is given by \( y = a|x| \), where \( a \) in this case is 3, modifying the equation to \( y = 3|x| \). However, this does not affect the x-coordinate of the vertex. 2. **Right Horizontal Shift of 2 Units:** - This shift moves the graph in the positive x-direction modifying the equation further to \( y = 3|x - 2| \). - The x-coordinate of the vertex moves from 0 to 2. 3. **Vertical Shift Downwards by 6 Units:** - This translates the graph downward, modifying the equation to \( y = 3|x - 2| - 6 \). - The y-coordinate of the vertex moves from 0 to -6. **Initial Vertex (Original graph of \( y = |x| \)):** - \((0, 0)\) **New Vertex:** - After applying the transformations, the new vertex is at \((2, -6)\). ### Correct Answer: - **(2, -6)**
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