What is the end behavior of f(x)? y 4677.75 4093.03 3508.31 2923.59 2338.88 1754.16 1169.44 584.77 -10 -98 -7 -6 -5 -4-3-2-1 -581.72 1 2 3 4 5 6 8 9
What is the end behavior of f(x)? y 4677.75 4093.03 3508.31 2923.59 2338.88 1754.16 1169.44 584.77 -10 -98 -7 -6 -5 -4-3-2-1 -581.72 1 2 3 4 5 6 8 9
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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What's the end behavior of f(x)
![**The graph of \(y = f(x)\) is below. What is the end behavior of \(f(x)\)?**
![Graph]
The given image shows the graph of the function \( y = f(x) \) plotted on an \( xy \)-coordinate system. The \( y \)-axis ranges approximately from -4677.75 to 4677.75, while the \( x \)-axis ranges from -10 to 10. The graph depicts a polynomial function that shows numerous oscillations.
**Detailed Explanation of the Graph:**
- Moving from left to right:
- The function starts in the upper left quadrant declining sharply, passing through the x-axis around \( x = -7 \), and continues to decrease.
- It then rises, creating a local peak near \( x = -4 \).
- The function then declines sharply again, reaching another local minimum.
- Thereafter, the function increases again creating another local peak around \( x = 0 \) to \( x = 1 \).
- It dips slightly before ascending sharply.
- Another oscillation occurs as the function dips before \( x = 5 \) and then rises steeply in an increasing direction as \( x \) continues to increase.
**Observations:**
- As \( x \to \infty \), \( f(x) \) increases without bound.
- As \( x \to -\infty \), \( f(x) \) decreases without bound.
### Multiple-Choice Responses:
- \( \bigcirc \) as \( x \to \infty \), \( f(x) \to -\infty \) and as \( x \to -\infty \), \( f(x) \to -\infty \)
- \( \bigcirc \) as \( x \to \infty \), \( f(x) \to \infty \) and as \( x \to -\infty \), \( f(x) \to \infty \)
- \( \bigcirc \) as \( x \to \infty \), \( f(x) \to \infty \) and as \( x \to -\infty \), \( f(x) \to -\infty \)
- \( \bigcirc \) as \( x \to \infty \), \( f(x) \to -\infty \) and as \( x \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe42523fa-6639-4055-8277-f7ddf19ef103%2F7e5345d4-0c8c-4b6e-862e-92eef10e1902%2Fstf26u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**The graph of \(y = f(x)\) is below. What is the end behavior of \(f(x)\)?**
![Graph]
The given image shows the graph of the function \( y = f(x) \) plotted on an \( xy \)-coordinate system. The \( y \)-axis ranges approximately from -4677.75 to 4677.75, while the \( x \)-axis ranges from -10 to 10. The graph depicts a polynomial function that shows numerous oscillations.
**Detailed Explanation of the Graph:**
- Moving from left to right:
- The function starts in the upper left quadrant declining sharply, passing through the x-axis around \( x = -7 \), and continues to decrease.
- It then rises, creating a local peak near \( x = -4 \).
- The function then declines sharply again, reaching another local minimum.
- Thereafter, the function increases again creating another local peak around \( x = 0 \) to \( x = 1 \).
- It dips slightly before ascending sharply.
- Another oscillation occurs as the function dips before \( x = 5 \) and then rises steeply in an increasing direction as \( x \) continues to increase.
**Observations:**
- As \( x \to \infty \), \( f(x) \) increases without bound.
- As \( x \to -\infty \), \( f(x) \) decreases without bound.
### Multiple-Choice Responses:
- \( \bigcirc \) as \( x \to \infty \), \( f(x) \to -\infty \) and as \( x \to -\infty \), \( f(x) \to -\infty \)
- \( \bigcirc \) as \( x \to \infty \), \( f(x) \to \infty \) and as \( x \to -\infty \), \( f(x) \to \infty \)
- \( \bigcirc \) as \( x \to \infty \), \( f(x) \to \infty \) and as \( x \to -\infty \), \( f(x) \to -\infty \)
- \( \bigcirc \) as \( x \to \infty \), \( f(x) \to -\infty \) and as \( x \
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