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Use the graph to identify zeros and multiplicity

Use the graph to identify zeros and multiplicity

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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Use the graph to identify zeros and multiplicity. ### Graph Explanation: The graph displays a polynomial function with the x-axis and y-axis labeled. The x-axis ranges from -5 to 5, and the y-axis ranges from -5 to 5. The curve shows distinct behavior at the x-intercepts. #### Key Features: - **Zeros (x-intercepts):** - The curve crosses the x-axis at three points. - Approximate zeros are: - At \( x = -3 \) - At \( x = -1 \) - At \( x = 2 \) - **Multiplicity:** - The graph crosses the x-axis at \( x = -3 \), indicating a zero with multiplicity of 1. - The graph touches or rebounds at \( x = -1 \), suggesting a higher multiplicity, likely 2. - The graph crosses through \( x = 2 \), indicating a zero with multiplicity of 1. The behavior of the graph at each intercept indicates the multiplicity of the zero, distinguishing between an even and odd multiplicity by whether the graph merely touches or passes through the x-axis.
Transcribed Image Text:Use the graph to identify zeros and multiplicity. ### Graph Explanation: The graph displays a polynomial function with the x-axis and y-axis labeled. The x-axis ranges from -5 to 5, and the y-axis ranges from -5 to 5. The curve shows distinct behavior at the x-intercepts. #### Key Features: - **Zeros (x-intercepts):** - The curve crosses the x-axis at three points. - Approximate zeros are: - At \( x = -3 \) - At \( x = -1 \) - At \( x = 2 \) - **Multiplicity:** - The graph crosses the x-axis at \( x = -3 \), indicating a zero with multiplicity of 1. - The graph touches or rebounds at \( x = -1 \), suggesting a higher multiplicity, likely 2. - The graph crosses through \( x = 2 \), indicating a zero with multiplicity of 1. The behavior of the graph at each intercept indicates the multiplicity of the zero, distinguishing between an even and odd multiplicity by whether the graph merely touches or passes through the x-axis.
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