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Vhich of the following figures below shows the graph of a polynomial which has the following zeros ir multiplicities: –1 (multiplicity 3), 4 (multiplicity 2)? Circle the correct answer. A B C

Vhich of the following figures below shows the graph of a polynomial which has the following zeros ir multiplicities: –1 (multiplicity 3), 4 (multiplicity 2)? Circle the correct answer. A B C

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:** Which of the following figures below shows the graph of a polynomial which has the following zeros and their multiplicities: \(-1\) (multiplicity 3), \(4\) (multiplicity 2)? Circle the correct answer. **Graphs:** - **A**: This graph appears to have a zero at \(-1\) where the graph touches the x-axis and flattens out, indicating this could be a zero with multiplicity 3. It appears to cross the x-axis around \(4\), which may suggest multiplicity 2, as it only touches and does not cross more dramatically. - **B**: This graph has a zero around \(-1\), but it crosses the x-axis sharply, suggesting a multiplicity of 1 or an even multiplicity not matching given conditions. It appears to have a zero around \(4\) but not with the required behavior for multiplicity 2. - **C**: This graph goes through the x-axis at \(-1\) but it does not appear to have the flattening effect associated with a zero of multiplicity 3. Around \(4\), the graph does not show a clear zero behavior. **Analysis:** The correct answer is **A** as it shows the appropriate characteristics of zeros at \(-1\) with multiplicity 3 and at \(4\) with multiplicity 2.
Transcribed Image Text:**Question:** Which of the following figures below shows the graph of a polynomial which has the following zeros and their multiplicities: \(-1\) (multiplicity 3), \(4\) (multiplicity 2)? Circle the correct answer. **Graphs:** - **A**: This graph appears to have a zero at \(-1\) where the graph touches the x-axis and flattens out, indicating this could be a zero with multiplicity 3. It appears to cross the x-axis around \(4\), which may suggest multiplicity 2, as it only touches and does not cross more dramatically. - **B**: This graph has a zero around \(-1\), but it crosses the x-axis sharply, suggesting a multiplicity of 1 or an even multiplicity not matching given conditions. It appears to have a zero around \(4\) but not with the required behavior for multiplicity 2. - **C**: This graph goes through the x-axis at \(-1\) but it does not appear to have the flattening effect associated with a zero of multiplicity 3. Around \(4\), the graph does not show a clear zero behavior. **Analysis:** The correct answer is **A** as it shows the appropriate characteristics of zeros at \(-1\) with multiplicity 3 and at \(4\) with multiplicity 2.
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