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Which of the following is a polynomial function that might have the given graph? O A. f(x) = 2x(x+ 3)2 (x - 3)2 O B. f(x) = - 2x(x- 3)2(x-3)2 O C. f(x) = 2x(x+3)(x-3) O D. f(x) = - 2x(x+3)2 (x+ 3)2 O E. f(x) = - 2x(x+3)2(x-3)2 O F. f(x) = - 2x(x+3)(x- 3)

Which of the following is a polynomial function that might have the given graph? O A. f(x) = 2x(x+ 3)2 (x - 3)2 O B. f(x) = - 2x(x- 3)2(x-3)2 O C. f(x) = 2x(x+3)(x-3) O D. f(x) = - 2x(x+3)2 (x+ 3)2 O E. f(x) = - 2x(x+3)2(x-3)2 O F. f(x) = - 2x(x+3)(x- 3)

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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The image presents a multiple-choice question regarding polynomial functions: **Question:** Which of the following is a polynomial function that might have the given graph? **Options:** - **A.** \( f(x) = 2x(x + 3)^2(x - 3)^2 \) - **B.** \( f(x) = -2x(x - 3)^2(x - 3)^2 \) - **C.** \( f(x) = 2x(x + 3)(x - 3) \) - **D.** \( f(x) = -2x(x + 3)^2(x + 3)^2 \) - **E.** \( f(x) = -2x(x + 3)^2(x - 3)^2 \) - **F.** \( f(x) = -2x(x + 3)(x - 3) \) Note: The graph that corresponds to these polynomial functions is not shown in the image.
Transcribed Image Text:The image presents a multiple-choice question regarding polynomial functions: **Question:** Which of the following is a polynomial function that might have the given graph? **Options:** - **A.** \( f(x) = 2x(x + 3)^2(x - 3)^2 \) - **B.** \( f(x) = -2x(x - 3)^2(x - 3)^2 \) - **C.** \( f(x) = 2x(x + 3)(x - 3) \) - **D.** \( f(x) = -2x(x + 3)^2(x + 3)^2 \) - **E.** \( f(x) = -2x(x + 3)^2(x - 3)^2 \) - **F.** \( f(x) = -2x(x + 3)(x - 3) \) Note: The graph that corresponds to these polynomial functions is not shown in the image.
**Problem Statement:** Write a polynomial function whose graph is shown below (use the smallest degree possible). The coordinates of the indicated point are \((-2, 100)\). **Graph Explanation:** The graph depicts a polynomial curve plotted on a Cartesian plane with both x and y axes labeled and equally spaced. The x-axis ranges from -5 to 5, while the y-axis spans from -150 to 150. Key Features of the Graph: - The curve crosses the y-axis upward at approximately 20. - There are turning points indicating local maximums and minimums; the curve has a local maximum at around \(x = -1.5, y = 90\) and a local minimum around \(x = 2.5, y = -120\). - There is an indicated specific point on the graph at \((-2, 100)\). - The curve represents fluctuations typical of a polynomial of degree at least 3, as observed from the number of turning points. The task is to determine a polynomial equation that fits this graph, taking into account its characteristics and the coordinates provided.
Transcribed Image Text:**Problem Statement:** Write a polynomial function whose graph is shown below (use the smallest degree possible). The coordinates of the indicated point are \((-2, 100)\). **Graph Explanation:** The graph depicts a polynomial curve plotted on a Cartesian plane with both x and y axes labeled and equally spaced. The x-axis ranges from -5 to 5, while the y-axis spans from -150 to 150. Key Features of the Graph: - The curve crosses the y-axis upward at approximately 20. - There are turning points indicating local maximums and minimums; the curve has a local maximum at around \(x = -1.5, y = 90\) and a local minimum around \(x = 2.5, y = -120\). - There is an indicated specific point on the graph at \((-2, 100)\). - The curve represents fluctuations typical of a polynomial of degree at least 3, as observed from the number of turning points. The task is to determine a polynomial equation that fits this graph, taking into account its characteristics and the coordinates provided.
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