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Find a system of inequalities whose graph is shown. ?v x ?v y?v (smaller slope) y?v (larger slope)

Find a system of inequalities whose graph is shown. ?v x ?v y?v (smaller slope) y?v (larger slope)

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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**Title: Understanding Systems of Inequalities through Graph Analysis** **Description:** This educational section helps students understand how to derive a system of inequalities from a given graph. The graph shows a shaded region representing the solutions to a system of inequalities. **Interactive Inputs for Inequalities:** - The task is to fill in the boxes to specify the system of inequalities based on the given graph. 1. **Inequality Components:** - First inequality: ___ ? ___ x ? ___ - Second inequality (smaller slope): y ? ___ (smaller slope) - Third inequality (larger slope): y ? ___ (larger slope) **Graph Description:** - **Axes:** The graph is marked with both x and y-axes. The axes intersect at the origin (0,0), extending from -5 to 5 for both x and y. - **Lines:** The graph consists of three lines: - A vertical dashed line at x = -1. - A solid line with a positive slope passing through the origin. - A solid line with a negative slope, intersecting the positive slope line and forming a triangular shaded region. - **Shaded Region:** A blue triangular area is shaded on the graph, indicating the solution set satisfying all the inequalities simultaneously. - **Slopes:** - The smaller slope line appears less steep than the larger slope line. - The point of intersection of these lines and the vertical dashed line marks the vertices of the shaded triangle. **Objective:** Identify the inequalities that correspond to the boundaries of the shaded region, ensuring both slope and intercept are accurate. **Functionality:** - Use dropdown menus and input boxes to form the correct inequalities. - Test understanding by visualizing how each inequality influences the shaded region on the graph. This exercise is ideal for students learning to connect algebraic expressions and graphical representations in linear inequalities.
Transcribed Image Text:**Title: Understanding Systems of Inequalities through Graph Analysis** **Description:** This educational section helps students understand how to derive a system of inequalities from a given graph. The graph shows a shaded region representing the solutions to a system of inequalities. **Interactive Inputs for Inequalities:** - The task is to fill in the boxes to specify the system of inequalities based on the given graph. 1. **Inequality Components:** - First inequality: ___ ? ___ x ? ___ - Second inequality (smaller slope): y ? ___ (smaller slope) - Third inequality (larger slope): y ? ___ (larger slope) **Graph Description:** - **Axes:** The graph is marked with both x and y-axes. The axes intersect at the origin (0,0), extending from -5 to 5 for both x and y. - **Lines:** The graph consists of three lines: - A vertical dashed line at x = -1. - A solid line with a positive slope passing through the origin. - A solid line with a negative slope, intersecting the positive slope line and forming a triangular shaded region. - **Shaded Region:** A blue triangular area is shaded on the graph, indicating the solution set satisfying all the inequalities simultaneously. - **Slopes:** - The smaller slope line appears less steep than the larger slope line. - The point of intersection of these lines and the vertical dashed line marks the vertices of the shaded triangle. **Objective:** Identify the inequalities that correspond to the boundaries of the shaded region, ensuring both slope and intercept are accurate. **Functionality:** - Use dropdown menus and input boxes to form the correct inequalities. - Test understanding by visualizing how each inequality influences the shaded region on the graph. This exercise is ideal for students learning to connect algebraic expressions and graphical representations in linear inequalities.
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