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Consider the following equations. y x-4 y = -x + 3 x = 0 x = 2 Sketch and shade the region bounded by the graphs of the functions. (Use solid lines for the boundaries.)

Consider the following equations. y x-4 y = -x + 3 x = 0 x = 2 Sketch and shade the region bounded by the graphs of the functions. (Use solid lines for the boundaries.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Equations and Graphing Activity** **Consider the Following Equations:** 1. \( y = x^2 - 4 \) 2. \( y = -x + 3 \) 3. \( x = 0 \) 4. \( x = 2 \) **Instructions:** 1. Sketch and shade the region bounded by the graphs of the functions. Use solid lines for the boundaries. 2. **Graph Details:** - The graph displays a coordinate grid with the x-axis ranging from -2 to 3 and the y-axis ranging from -5 to 10. - The quadratic function \( y = x^2 - 4 \) will form a parabola opening upwards with its vertex at (0, -4). - The linear function \( y = -x + 3 \) is a straight line with a y-intercept at (0, 3) and a slope of -1. - The vertical lines \( x = 0 \) and \( x = 2 \) will form boundaries for the shaded region on the graph. 3. Use the graphing tools to accurately represent the functions and identify the bounded region. 4. **Objective:** - Find the area of the shaded region. **Graph Layers:** - After you add an object to the graph, you can use Graph Layers to view and edit its properties. **Task:** - Complete the activity by determining the area of the region enclosed by the graphs.
Transcribed Image Text:**Equations and Graphing Activity** **Consider the Following Equations:** 1. \( y = x^2 - 4 \) 2. \( y = -x + 3 \) 3. \( x = 0 \) 4. \( x = 2 \) **Instructions:** 1. Sketch and shade the region bounded by the graphs of the functions. Use solid lines for the boundaries. 2. **Graph Details:** - The graph displays a coordinate grid with the x-axis ranging from -2 to 3 and the y-axis ranging from -5 to 10. - The quadratic function \( y = x^2 - 4 \) will form a parabola opening upwards with its vertex at (0, -4). - The linear function \( y = -x + 3 \) is a straight line with a y-intercept at (0, 3) and a slope of -1. - The vertical lines \( x = 0 \) and \( x = 2 \) will form boundaries for the shaded region on the graph. 3. Use the graphing tools to accurately represent the functions and identify the bounded region. 4. **Objective:** - Find the area of the shaded region. **Graph Layers:** - After you add an object to the graph, you can use Graph Layers to view and edit its properties. **Task:** - Complete the activity by determining the area of the region enclosed by the graphs.
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