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Write a cubic function whose graph is shown. 4 1 (0, 2) -1,0) (2, 0) -4 -2 4 x (1, 0) f(x) =

Write a cubic function whose graph is shown. 4 1 (0, 2) -1,0) (2, 0) -4 -2 4 x (1, 0) f(x) =

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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**Write a cubic function whose graph is shown.** The graph presented is a cubic function, which has a distinct S-shape. Key features of this graph include: - **Y-intercept**: The graph crosses the y-axis at (0, 2). - **X-intercepts (roots)**: The graph crosses the x-axis at three points: (-1, 0), (1, 0), and (2, 0). - **Turning points**: The graph has turning points indicative of the cubic nature of the function, starting from the bottom left, moving upwards, and then dipping before continuing upwards on the right. **Coordinate Grid**: - The x-axis ranges from -4 to 4. - The y-axis ranges from -4 to 4. **Equation**: The function \( f(x) = \square \) represents the equation of the cubic graph. The specific terms of the function need to be completed or derived based on the intercepts and critical points shown on the graph.
Transcribed Image Text:**Write a cubic function whose graph is shown.** The graph presented is a cubic function, which has a distinct S-shape. Key features of this graph include: - **Y-intercept**: The graph crosses the y-axis at (0, 2). - **X-intercepts (roots)**: The graph crosses the x-axis at three points: (-1, 0), (1, 0), and (2, 0). - **Turning points**: The graph has turning points indicative of the cubic nature of the function, starting from the bottom left, moving upwards, and then dipping before continuing upwards on the right. **Coordinate Grid**: - The x-axis ranges from -4 to 4. - The y-axis ranges from -4 to 4. **Equation**: The function \( f(x) = \square \) represents the equation of the cubic graph. The specific terms of the function need to be completed or derived based on the intercepts and critical points shown on the graph.
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