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(a) The graph of y=f (x) is shown. Graph y= (x). 8. 6+ 4 -8 -6 -4 -2 6. 8. -2 -4 -6 -8 4. 2. 2.

(a) The graph of y=f (x) is shown. Graph y= (x). 8. 6+ 4 -8 -6 -4 -2 6. 8. -2 -4 -6 -8 4. 2. 2.

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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I am supposed to transform each graph as specified below (see screenshots). How do I do that? Thank you ! 

**Topic: Transforming the Graph of a Function by Shrinking or Stretching** **Transcription and Explanation:** (a) The graph of \( y = f(x) \) is shown. Graph \( y = \frac{1}{2}f(x) \). **Graph Description:** The graph displayed is a piecewise linear function resembling a "V" shape, typical of an absolute value function. It is positioned on a standard Cartesian coordinate grid with x and y axes ranging from -8 to 8. - The vertex of the V is at the point (-2, 0). - The left arm of the V extends downward at a 45-degree angle, passing through the point (-4, -2). - The right arm of the V extends upwards at a 45-degree angle, passing through the point (0, 2). **Transformation Explanation:** To transform the function \( y = f(x) \) into \( y = \frac{1}{2}f(x) \), you vertically shrink the graph by a factor of \(\frac{1}{2}\). This means that each y-coordinate of the original graph will be halved, whereas the x-coordinates remain unchanged. **Interactive Tools Explanation:** The interface includes several interactive tools: - **Eraser icon**: Likely used for removing sections of the graph or resetting changes. - **Pencil icon**: Possibly for drawing or annotating on the graph. - **Line icon**: Could be used to draw straight lines to assist in transformations. - **Grid icon**: May toggle the visibility of the grid. - **Check button**: To verify if the transformation has been applied correctly. - **Explanation button**: Provides more details or solutions related to the exercise. - **Undo icon**: Allows reversal of recent actions taken on the graph. - **Question mark icon**: Offers help or tips for using the interface and understanding the task. To visualize the transformation correctly, consider how each point on the graph will change. For instance, a point originally at (-4, -2) will move to (-4, -1), and a point at (0, 2) will become (0, 1) after applying the vertical shrink.
Transcribed Image Text:**Topic: Transforming the Graph of a Function by Shrinking or Stretching** **Transcription and Explanation:** (a) The graph of \( y = f(x) \) is shown. Graph \( y = \frac{1}{2}f(x) \). **Graph Description:** The graph displayed is a piecewise linear function resembling a "V" shape, typical of an absolute value function. It is positioned on a standard Cartesian coordinate grid with x and y axes ranging from -8 to 8. - The vertex of the V is at the point (-2, 0). - The left arm of the V extends downward at a 45-degree angle, passing through the point (-4, -2). - The right arm of the V extends upwards at a 45-degree angle, passing through the point (0, 2). **Transformation Explanation:** To transform the function \( y = f(x) \) into \( y = \frac{1}{2}f(x) \), you vertically shrink the graph by a factor of \(\frac{1}{2}\). This means that each y-coordinate of the original graph will be halved, whereas the x-coordinates remain unchanged. **Interactive Tools Explanation:** The interface includes several interactive tools: - **Eraser icon**: Likely used for removing sections of the graph or resetting changes. - **Pencil icon**: Possibly for drawing or annotating on the graph. - **Line icon**: Could be used to draw straight lines to assist in transformations. - **Grid icon**: May toggle the visibility of the grid. - **Check button**: To verify if the transformation has been applied correctly. - **Explanation button**: Provides more details or solutions related to the exercise. - **Undo icon**: Allows reversal of recent actions taken on the graph. - **Question mark icon**: Offers help or tips for using the interface and understanding the task. To visualize the transformation correctly, consider how each point on the graph will change. For instance, a point originally at (-4, -2) will move to (-4, -1), and a point at (0, 2) will become (0, 1) after applying the vertical shrink.
The image presents an exercise from a platform named ALEKS, focused on trigonometry. The task is as follows: **Task:** (b) The graph of \( y = g(x) \) is shown. Graph \( y = g\left(\frac{1}{2}x\right) \). **Graph Description:** The graph provided is a V-shaped plot, resembling an absolute value function, centered at the origin (0,0) on a coordinate plane. - **Axes:** - The horizontal axis is the \( x \)-axis, ranging from -8 to 8. - The vertical axis is the \( y \)-axis, ranging from -8 to 8. - **Function:** - The function is symmetric about the y-axis, indicating a typical absolute value or piecewise linear function. - The graph passes through points like (0,0), (1,1), (-1,1), indicating a possible absolute value function \( y = |x| \). **Objective:** - The task is to graph \( y = g\left(\frac{1}{2}x\right) \), which indicates a horizontal stretch of the original function by a factor of 2. This means for every x-value of the original graph, the corresponding x-value in the new graph is divided by 2, stretching the graph away from the y-axis.
Transcribed Image Text:The image presents an exercise from a platform named ALEKS, focused on trigonometry. The task is as follows: **Task:** (b) The graph of \( y = g(x) \) is shown. Graph \( y = g\left(\frac{1}{2}x\right) \). **Graph Description:** The graph provided is a V-shaped plot, resembling an absolute value function, centered at the origin (0,0) on a coordinate plane. - **Axes:** - The horizontal axis is the \( x \)-axis, ranging from -8 to 8. - The vertical axis is the \( y \)-axis, ranging from -8 to 8. - **Function:** - The function is symmetric about the y-axis, indicating a typical absolute value or piecewise linear function. - The graph passes through points like (0,0), (1,1), (-1,1), indicating a possible absolute value function \( y = |x| \). **Objective:** - The task is to graph \( y = g\left(\frac{1}{2}x\right) \), which indicates a horizontal stretch of the original function by a factor of 2. This means for every x-value of the original graph, the corresponding x-value in the new graph is divided by 2, stretching the graph away from the y-axis.
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