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Graph and shade the domain of f(x, y) = vy + x² – 2.

Graph and shade the domain of f(x, y) = vy + x² – 2.

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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**Exercise: Graph and Analyze the Domain** 1. **Problem Statement:** - Graph and shade the domain of the function \( f(x, y) = \sqrt{y + x^2 - 2} \). 2. **Solution Steps:** - To determine the domain of the function, identify where the expression under the square root is non-negative. - Set up the inequality: \( y + x^2 - 2 \geq 0 \). - Rearrange to find \( y \geq -x^2 + 2 \). - The domain consists of all points \((x, y)\) in the coordinate plane that satisfy \( y \geq -x^2 + 2 \). 3. **Graph Explanation:** - The inequality \( y \geq -x^2 + 2 \) represents the region above (and including) the parabola \( y = -x^2 + 2 \). - This parabola opens downwards with a vertex at \((0, 2)\). - Shade the region above the parabola to illustrate the domain of the function. **Conclusion:** The domain is the set of all points \((x, y)\) within and on the boundary defined by the inequality above.
Transcribed Image Text:**Exercise: Graph and Analyze the Domain** 1. **Problem Statement:** - Graph and shade the domain of the function \( f(x, y) = \sqrt{y + x^2 - 2} \). 2. **Solution Steps:** - To determine the domain of the function, identify where the expression under the square root is non-negative. - Set up the inequality: \( y + x^2 - 2 \geq 0 \). - Rearrange to find \( y \geq -x^2 + 2 \). - The domain consists of all points \((x, y)\) in the coordinate plane that satisfy \( y \geq -x^2 + 2 \). 3. **Graph Explanation:** - The inequality \( y \geq -x^2 + 2 \) represents the region above (and including) the parabola \( y = -x^2 + 2 \). - This parabola opens downwards with a vertex at \((0, 2)\). - Shade the region above the parabola to illustrate the domain of the function. **Conclusion:** The domain is the set of all points \((x, y)\) within and on the boundary defined by the inequality above.
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