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Use the graph y=f(x) to graph the given function. y = f(x) -8 -6 y = -— -f(x) -2 + -2 10 6 1. 2 4 6 8

Use the graph y=f(x) to graph the given function. y = f(x) -8 -6 y = -— -f(x) -2 + -2 10 6 1. 2 4 6 8

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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Use the graph y=f(x) to graph the given function
**Transcription for Educational Website** **Task: Graphing a Function** "Use the graph \( y = f(x) \) to graph the given function." **Graph 1: \( y = f(x) \)** - The graph is a blue triangle-shaped plot on a Cartesian plane. - The x-axis and y-axis range from -8 to 8. - The function forms a V-shape, with the vertex at the point (0, 8). - The function intercepts the x-axis at (-8, 0) and (8, 0), indicating these are the roots. **Graph 2: \( y = \frac{1}{9}f(x) \)** - This graph is currently not plotted, represented as an empty coordinate plane. - The axes range from -8 to 8 on both the x and y scales, just like the first graph. **Explanation: Transformation of the Function** The task involves transforming the original function \( y = f(x) \) by scaling it vertically. The function \( y = \frac{1}{9}f(x) \) represents a vertical compression by a factor of \(\frac{1}{9}\). This transformation will reduce the height of each point on the graph \( y = f(x) \) to \(\frac{1}{9}\) of its original value. Hence, the graph that currently peaks at 8 will peak at \(\frac{8}{9}\). **Steps to Graph \( y = \frac{1}{9}f(x) \):** 1. Identify key points on the original graph, such as the vertex and x-intercepts. 2. Multiply the y-coordinate of each point by \(\frac{1}{9}\). 3. Plot the transformed points and connect them to maintain the V-shape. This exercise demonstrates how transformations affect the shape and position of graphs in the coordinate system.
Transcribed Image Text:**Transcription for Educational Website** **Task: Graphing a Function** "Use the graph \( y = f(x) \) to graph the given function." **Graph 1: \( y = f(x) \)** - The graph is a blue triangle-shaped plot on a Cartesian plane. - The x-axis and y-axis range from -8 to 8. - The function forms a V-shape, with the vertex at the point (0, 8). - The function intercepts the x-axis at (-8, 0) and (8, 0), indicating these are the roots. **Graph 2: \( y = \frac{1}{9}f(x) \)** - This graph is currently not plotted, represented as an empty coordinate plane. - The axes range from -8 to 8 on both the x and y scales, just like the first graph. **Explanation: Transformation of the Function** The task involves transforming the original function \( y = f(x) \) by scaling it vertically. The function \( y = \frac{1}{9}f(x) \) represents a vertical compression by a factor of \(\frac{1}{9}\). This transformation will reduce the height of each point on the graph \( y = f(x) \) to \(\frac{1}{9}\) of its original value. Hence, the graph that currently peaks at 8 will peak at \(\frac{8}{9}\). **Steps to Graph \( y = \frac{1}{9}f(x) \):** 1. Identify key points on the original graph, such as the vertex and x-intercepts. 2. Multiply the y-coordinate of each point by \(\frac{1}{9}\). 3. Plot the transformed points and connect them to maintain the V-shape. This exercise demonstrates how transformations affect the shape and position of graphs in the coordinate system.
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