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Ny 8- X= y. x= | y2 - 6 -10 10

Ny 8- X= y. x= | y2 - 6 -10 10

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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Question

The area of the given figure is

​(Round to the nearest two decimal places as​ needed.)

The image shows a coordinate plane with two graphed equations and a shaded region. 1. **Graph Details:** - The x-axis and y-axis are labeled and range from -10 to 10. - A red line represents the equation \( x = y \). This line passes through the origin and has a 45-degree angle, indicating a direct proportionality between x and y. - A blue curve represents the equation \( x = y^2 - 6 \). This is a sideways parabola, opening horizontally. The vertex of the parabola is at the point (-6, 0), and it intersects the x-axis at this point. The parabola is symmetric about the y-axis and crosses it at two points. 2. **Shaded Region:** - There is a grey shaded area between the red line and the blue curve. This region represents the set of points that are bounded by the equations \( x = y \) and \( x = y^2 - 6 \). This diagram helps visualize the relationship and intersection between a linear function and a quadratic function on a coordinate plane.
Transcribed Image Text:The image shows a coordinate plane with two graphed equations and a shaded region. 1. **Graph Details:** - The x-axis and y-axis are labeled and range from -10 to 10. - A red line represents the equation \( x = y \). This line passes through the origin and has a 45-degree angle, indicating a direct proportionality between x and y. - A blue curve represents the equation \( x = y^2 - 6 \). This is a sideways parabola, opening horizontally. The vertex of the parabola is at the point (-6, 0), and it intersects the x-axis at this point. The parabola is symmetric about the y-axis and crosses it at two points. 2. **Shaded Region:** - There is a grey shaded area between the red line and the blue curve. This region represents the set of points that are bounded by the equations \( x = y \) and \( x = y^2 - 6 \). This diagram helps visualize the relationship and intersection between a linear function and a quadratic function on a coordinate plane.
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