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Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient. deg: coeff: deg: coeff: deg: NA coeff: W WA deg: coeff: Stuy

Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient. deg: coeff: deg: coeff: deg: NA coeff: W WA deg: coeff: Stuy

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Title:** Identifying Polynomial Functions by Degree and Leading Coefficient **Instructions:** Analyze the graphs below to determine if the function graphed has an odd or even degree and if the leading coefficient is positive or negative. **Graph Analysis:** 1. **Top Left Graph:** - The graph appears to start from the bottom left and rise to the top right. - **Degree (deg):** Odd (since the ends of the graph go in opposite directions) - **Leading Coefficient (coeff):** Positive (since the graph rises to the right) 2. **Top Right Graph:** - The graph starts and ends downward, passing through the x-axis in the middle. - **Degree (deg):** Even (since both ends of the graph go in the same direction, down) - **Leading Coefficient (coeff):** Negative (since the graph ends downward) 3. **Bottom Left Graph:** - The graph starts and ends upward, dipping down in between. - **Degree (deg):** Even (since both ends of the graph go in the same direction, up) - **Leading Coefficient (coeff):** Positive (since the graph ends upward) 4. **Bottom Right Graph:** - The graph starts from the top left and falls to the bottom right. - **Degree (deg):** Odd (since the ends of the graph go in opposite directions) - **Leading Coefficient (coeff):** Negative (since the graph falls to the right) **Conclusion:** By observing the directionality of the graph ends and their behavior across the x-axis, it is possible to determine the degree and the sign of the leading coefficient for each polynomial function presented. Use these characteristics to analyze polynomial functions effectively.
Transcribed Image Text:**Title:** Identifying Polynomial Functions by Degree and Leading Coefficient **Instructions:** Analyze the graphs below to determine if the function graphed has an odd or even degree and if the leading coefficient is positive or negative. **Graph Analysis:** 1. **Top Left Graph:** - The graph appears to start from the bottom left and rise to the top right. - **Degree (deg):** Odd (since the ends of the graph go in opposite directions) - **Leading Coefficient (coeff):** Positive (since the graph rises to the right) 2. **Top Right Graph:** - The graph starts and ends downward, passing through the x-axis in the middle. - **Degree (deg):** Even (since both ends of the graph go in the same direction, down) - **Leading Coefficient (coeff):** Negative (since the graph ends downward) 3. **Bottom Left Graph:** - The graph starts and ends upward, dipping down in between. - **Degree (deg):** Even (since both ends of the graph go in the same direction, up) - **Leading Coefficient (coeff):** Positive (since the graph ends upward) 4. **Bottom Right Graph:** - The graph starts from the top left and falls to the bottom right. - **Degree (deg):** Odd (since the ends of the graph go in opposite directions) - **Leading Coefficient (coeff):** Negative (since the graph falls to the right) **Conclusion:** By observing the directionality of the graph ends and their behavior across the x-axis, it is possible to determine the degree and the sign of the leading coefficient for each polynomial function presented. Use these characteristics to analyze polynomial functions effectively.
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