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
graph the inequality
![The inequality shown in the image is:
\[ y - x^2 > 2 \]
This describes a region in the coordinate plane. Specifically, it represents the set of all points \((x, y)\) for which the \( y \) value is greater than \( x^2 + 2 \).
In more detail:
- \( x^2 \): This term represents a parabolic curve with its vertex at the origin \((0,0)\) and opening upwards.
- \( + 2 \): This shifts the entire parabola upwards by 2 units.
- The inequality \(>\) indicates that we are interested in the region above this parabola.
Graphically, this would be represented by shading the area above the parabola defined by \( y = x^2 + 2 \). The boundary itself, \( y = x^2 + 2 \), is not included in this region since the inequality is strictly greater than (\(>\)) and not greater than or equal to (\(\geq\)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f130582-8262-45ba-b1cd-6680cc0034f3%2F764df5ff-6a84-4ab6-8332-5097534efd53%2F97av3l6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The inequality shown in the image is:
\[ y - x^2 > 2 \]
This describes a region in the coordinate plane. Specifically, it represents the set of all points \((x, y)\) for which the \( y \) value is greater than \( x^2 + 2 \).
In more detail:
- \( x^2 \): This term represents a parabolic curve with its vertex at the origin \((0,0)\) and opening upwards.
- \( + 2 \): This shifts the entire parabola upwards by 2 units.
- The inequality \(>\) indicates that we are interested in the region above this parabola.
Graphically, this would be represented by shading the area above the parabola defined by \( y = x^2 + 2 \). The boundary itself, \( y = x^2 + 2 \), is not included in this region since the inequality is strictly greater than (\(>\)) and not greater than or equal to (\(\geq\)).
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