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(f) y - f(x) - 10 y 15 10 5 -15 - 10 -5 10 15 -15 - 10 -5 10 15 10 - 10 -15 -15 y 15 15 10 10 WebAssign Plot -15 - 10 -5 10 15 -15/ - 10 10 15 -5 -10 - 10 -15 -15

(f) y - f(x) - 10 y 15 10 5 -15 - 10 -5 10 15 -15 - 10 -5 10 15 10 - 10 -15 -15 y 15 15 10 10 WebAssign Plot -15 - 10 -5 10 15 -15/ - 10 10 15 -5 -10 - 10 -15 -15

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Transcription:** "Use the graph of \( f \) to sketch each graph." **Graph Explanation:** The graph represents a function \( f \) with a smooth curve. Key points on the graph are noted as follows: - The graph has a peak at the point \((0, 5)\). - It intersects the x-axis at \((-3, 0)\) and \((3, 0)\). - The graph has endpoints at \((-6, -4)\) and \((6, -4)\). **Description of the Curve:** - The curve starts at the point \((-6, -4)\) on the left side, moves upward to reach \((-3, 0)\), continues to rise reaching its maximum height at \((0, 5)\), then symmetrically descends passing through \((3, 0)\), and finally ends at \((6, -4)\). - The overall shape resembles an inverted parabola with horizontal symmetry about the y-axis.
Transcribed Image Text:**Transcription:** "Use the graph of \( f \) to sketch each graph." **Graph Explanation:** The graph represents a function \( f \) with a smooth curve. Key points on the graph are noted as follows: - The graph has a peak at the point \((0, 5)\). - It intersects the x-axis at \((-3, 0)\) and \((3, 0)\). - The graph has endpoints at \((-6, -4)\) and \((6, -4)\). **Description of the Curve:** - The curve starts at the point \((-6, -4)\) on the left side, moves upward to reach \((-3, 0)\), continues to rise reaching its maximum height at \((0, 5)\), then symmetrically descends passing through \((3, 0)\), and finally ends at \((6, -4)\). - The overall shape resembles an inverted parabola with horizontal symmetry about the y-axis.
The image displays four graphs representing the function transformation \( y = r(x) - 10 \). ### Description of the Graphs: 1. **Top-Left Graph:** - This graph represents a downward reflection across the horizontal axis. The main feature is a concave-up curve centered around the y-axis, shifted 10 units down along the y-axis. The curve peaks at approximately \(-10\) on the y-axis. 2. **Top-Right Graph:** - Here, the graph shows a curve with a concave-down shape centered around the y-axis, with a peak just below the horizontal axis, around \(-10\) on the y-axis. 3. **Bottom-Left Graph:** - The graph displays a downward-opening curve shifted to the right side of the y-axis, with its peak also near \(-10\) on the y-axis. 4. **Bottom-Right Graph:** - This graph shows the curve with a concave-down shape, positioned more towards the left side of the y-axis. Again, the peak is around \(-10\) on the y-axis. ### Observations: - All graphs portray transformations of a function, specifically vertical translations. - Each graph appears to illustrate shifts but have different orientations and central axes, demonstrating how subtraction of a value affects the position of \( r(x) \) along the y-axis.
Transcribed Image Text:The image displays four graphs representing the function transformation \( y = r(x) - 10 \). ### Description of the Graphs: 1. **Top-Left Graph:** - This graph represents a downward reflection across the horizontal axis. The main feature is a concave-up curve centered around the y-axis, shifted 10 units down along the y-axis. The curve peaks at approximately \(-10\) on the y-axis. 2. **Top-Right Graph:** - Here, the graph shows a curve with a concave-down shape centered around the y-axis, with a peak just below the horizontal axis, around \(-10\) on the y-axis. 3. **Bottom-Left Graph:** - The graph displays a downward-opening curve shifted to the right side of the y-axis, with its peak also near \(-10\) on the y-axis. 4. **Bottom-Right Graph:** - This graph shows the curve with a concave-down shape, positioned more towards the left side of the y-axis. Again, the peak is around \(-10\) on the y-axis. ### Observations: - All graphs portray transformations of a function, specifically vertical translations. - Each graph appears to illustrate shifts but have different orientations and central axes, demonstrating how subtraction of a value affects the position of \( r(x) \) along the y-axis.
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