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Below is the graph of a polynomial function with real coefficients. All local extrema of the 10 Use the graph to answer the following questions. (a) Over which intervals is the function increasing? Choose all that apply. o(-0, -2) o (-2, 3) (3, 7) (-2, 7) (7, o) (b) At which x-values does the function have local minima? If there is more than one value, separate them with commas. (c) What is the sign of the function's leading coefficient? (Choose one) (d) Which of the following is a possibility for the degree of the function? Choose all that apply. D4 6. 9

Below is the graph of a polynomial function with real coefficients. All local extrema of the 10 Use the graph to answer the following questions. (a) Over which intervals is the function increasing? Choose all that apply. o(-0, -2) o (-2, 3) (3, 7) (-2, 7) (7, o) (b) At which x-values does the function have local minima? If there is more than one value, separate them with commas. (c) What is the sign of the function's leading coefficient? (Choose one) (d) Which of the following is a possibility for the degree of the function? Choose all that apply. D4 6. 9

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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**Graph of a Polynomial Function** Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown. [Graph Description] - The graph displays a curve with two peaks and two valleys. - The x-axis ranges from -2 to 10, and the y-axis ranges from -4 to 4. - Local maxima occur approximately at x = -1 and x = 6. - Local minima occur approximately at x = 2 and x = 8. **Use the graph to answer the following questions:** (a) Over which intervals is the function increasing? Choose all that apply. - [ ] \((-∞, -2)\) - [x] \((-2, 3)\) - [ ] \((3, 7)\) - [ ] \((-2, 7)\) - [x] \((7, ∞)\) (b) At which x-values does the function have local minima? If there is more than one value, separate them with commas. - [Input Area] (c) What is the sign of the function’s leading coefficient? - [Dropdown Menu] (d) Which of the following is a possibility for the degree of the function? Choose all that apply. - [ ] 4 - [ ] 5 - [x] 6 - [ ] 7 - [x] 8 - [ ] 9 **Instructions for Educators:** - Discuss how to determine the increasing and decreasing intervals from the graph. - Explain how to identify local minima and maxima and relate them to the turning points. - Use this graph to demonstrate how the leading coefficient affects the end behavior of a polynomial. - Engage students in exploring possible polynomial degrees based on the number of turning points.
Transcribed Image Text:**Graph of a Polynomial Function** Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown. [Graph Description] - The graph displays a curve with two peaks and two valleys. - The x-axis ranges from -2 to 10, and the y-axis ranges from -4 to 4. - Local maxima occur approximately at x = -1 and x = 6. - Local minima occur approximately at x = 2 and x = 8. **Use the graph to answer the following questions:** (a) Over which intervals is the function increasing? Choose all that apply. - [ ] \((-∞, -2)\) - [x] \((-2, 3)\) - [ ] \((3, 7)\) - [ ] \((-2, 7)\) - [x] \((7, ∞)\) (b) At which x-values does the function have local minima? If there is more than one value, separate them with commas. - [Input Area] (c) What is the sign of the function’s leading coefficient? - [Dropdown Menu] (d) Which of the following is a possibility for the degree of the function? Choose all that apply. - [ ] 4 - [ ] 5 - [x] 6 - [ ] 7 - [x] 8 - [ ] 9 **Instructions for Educators:** - Discuss how to determine the increasing and decreasing intervals from the graph. - Explain how to identify local minima and maxima and relate them to the turning points. - Use this graph to demonstrate how the leading coefficient affects the end behavior of a polynomial. - Engage students in exploring possible polynomial degrees based on the number of turning points.
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