Write a cubic function whose graph is shown. AY A (-2, 4) 4 (2,0) -4 -2 4 x (-3,0) (-1, 0) -8 f(x) = D %3D
Write a cubic function whose graph is shown. AY A (-2, 4) 4 (2,0) -4 -2 4 x (-3,0) (-1, 0) -8 f(x) = D %3D
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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![**Task: Write a cubic function whose graph is shown.**
**Graph Analysis:**
The image shows a plot of a cubic function on a Cartesian coordinate grid.
- **Axes:** The x-axis and y-axis both range from -4 to 4; the y-axis extends further down to -8.
- **Points:**
- The graph passes through several key points:
- (-3, 0)
- (-1, 0)
- (2, 0)
- (-2, 4)
- **Behavior:**
- The cubic curve has intercepts at x = -3, x = -1, and x = 2, indicating these are the roots of the function.
- The graph shows an upward trend beyond x = 2 and trends downward as x becomes less than -3.
**Equation Form:**
The function is of the form \( f(x) = a(x + 3)(x + 1)(x - 2) \), where "a" is a constant. Given the point (-2, 4), you can substitute x and y values to solve for "a".
**Function Box:**
\[ f(x) = \text{(expression input field)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe67f5cb0-daee-4ea8-9bfc-4a00f267029a%2Fc24c561b-7e08-4510-ad90-2872fbc518b1%2Fi6weclm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Task: Write a cubic function whose graph is shown.**
**Graph Analysis:**
The image shows a plot of a cubic function on a Cartesian coordinate grid.
- **Axes:** The x-axis and y-axis both range from -4 to 4; the y-axis extends further down to -8.
- **Points:**
- The graph passes through several key points:
- (-3, 0)
- (-1, 0)
- (2, 0)
- (-2, 4)
- **Behavior:**
- The cubic curve has intercepts at x = -3, x = -1, and x = 2, indicating these are the roots of the function.
- The graph shows an upward trend beyond x = 2 and trends downward as x becomes less than -3.
**Equation Form:**
The function is of the form \( f(x) = a(x + 3)(x + 1)(x - 2) \), where "a" is a constant. Given the point (-2, 4), you can substitute x and y values to solve for "a".
**Function Box:**
\[ f(x) = \text{(expression input field)} \]
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