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The functions f(x) = x2 – 1 and g(x) = –x2 + 4 are shown on the graph. Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified? y > x2 – 1 y ≤ –x2 + 4

The functions f(x) = x2 – 1 and g(x) = –x2 + 4 are shown on the graph. Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified? y > x2 – 1 y ≤ –x2 + 4

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The functions f(x) = x2 – 1 and g(x) = –x2 + 4 are shown on the graph.

Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?

y > x2 – 1
y ≤ –x2 + 4

The image contains a graph with two quadratic functions, \( f(x) \) and \( g(x) \), plotted on the Cartesian plane. **Graph Details:** - **Axes:** - The x-axis and y-axis are labeled with numerical increments from -5 to 9 on the x-axis and -3 to 9 on the y-axis. - **Function \( f(x) = x^2 - 1 \):** - This is a parabola that opens upwards, shown in red. - The vertex of the parabola is at (0, -1). - The graph intersects the y-axis at -1 and the x-axis at approximately (-1, 0) and (1, 0). - **Function \( g(x) = -x^2 + 4 \):** - This is a parabola that opens downwards, shown in blue. - The vertex of the parabola is at (0, 4). - The graph intersects the y-axis at 4 and the x-axis at approximately (-2, 0) and (2, 0). **Interaction:** - The parabolas overlap between the y-values of -1 and 3 and intersect each other at points where the red and blue curves cross. This visualization helps in studying the properties of quadratic functions, their graphs, and points of intersection.
Transcribed Image Text:The image contains a graph with two quadratic functions, \( f(x) \) and \( g(x) \), plotted on the Cartesian plane. **Graph Details:** - **Axes:** - The x-axis and y-axis are labeled with numerical increments from -5 to 9 on the x-axis and -3 to 9 on the y-axis. - **Function \( f(x) = x^2 - 1 \):** - This is a parabola that opens upwards, shown in red. - The vertex of the parabola is at (0, -1). - The graph intersects the y-axis at -1 and the x-axis at approximately (-1, 0) and (1, 0). - **Function \( g(x) = -x^2 + 4 \):** - This is a parabola that opens downwards, shown in blue. - The vertex of the parabola is at (0, 4). - The graph intersects the y-axis at 4 and the x-axis at approximately (-2, 0) and (2, 0). **Interaction:** - The parabolas overlap between the y-values of -1 and 3 and intersect each other at points where the red and blue curves cross. This visualization helps in studying the properties of quadratic functions, their graphs, and points of intersection.
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