The graph of a function f(x) is given. Answer the question. f(x) e. v 5+ 4 3- -~~- 2- -2- -3- 345 Domain(f) ✓ Image(f) ✓ f(-1) If f(x) = 9, then x = ?
The graph of a function f(x) is given. Answer the question. f(x) e. v 5+ 4 3- -~~- 2- -2- -3- 345 Domain(f) ✓ Image(f) ✓ f(-1) If f(x) = 9, then x = ?
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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![**Question 2**
**The graph of a function \( f(x) \) is given. Answer the question.**
[Graph Description]
- The graph is of a curved function that appears to be a part of a parabola opening downwards.
- It intersects the y-axis at approximately \( y = 4 \).
- It reaches its maximum at \( (0, 4) \).
- The x-values where the graph is defined seem to be within \( x = -2 \) to \( x = 4 \).
**Graph Analysis**
- The x-axis represents the domain of the function.
- The y-axis represents the range (or image) of the function.
**Options to Determine**
- **Domain of \( f \)**:
- a. \( (-4, 5) \)
- b. 4
- c. 0
- d. \( (-\infty, \infty) \)
- e. \([-2, 4]\)
- f. \([-5, 4]\)
- g. \([-2, 4.1]\)
- h. Undefined
- **Image of \( f \)**:
- Not explicitly listed, but inferred from the graph.
**Evaluate Specific Values**
- **\( f(-1) \)**:
- Evaluate by identifying \( y \) when \( x = -1 \) on the graph.
- **If \( f(x) = 9 \), then \( x = ? \)**:
- Determine whether \( f(x) = 9 \) is possible by checking the graph's maximum point.
**Explanation**
The domain, image, and specific point evaluations help understand the nature and range of possible values for the function \( f(x) \) depicted by the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3332cd2-12f6-4e54-be20-e0f30e22e2a4%2Fe2e91e10-501d-4edd-8f21-77c1443f00db%2Frt7xyho_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 2**
**The graph of a function \( f(x) \) is given. Answer the question.**
[Graph Description]
- The graph is of a curved function that appears to be a part of a parabola opening downwards.
- It intersects the y-axis at approximately \( y = 4 \).
- It reaches its maximum at \( (0, 4) \).
- The x-values where the graph is defined seem to be within \( x = -2 \) to \( x = 4 \).
**Graph Analysis**
- The x-axis represents the domain of the function.
- The y-axis represents the range (or image) of the function.
**Options to Determine**
- **Domain of \( f \)**:
- a. \( (-4, 5) \)
- b. 4
- c. 0
- d. \( (-\infty, \infty) \)
- e. \([-2, 4]\)
- f. \([-5, 4]\)
- g. \([-2, 4.1]\)
- h. Undefined
- **Image of \( f \)**:
- Not explicitly listed, but inferred from the graph.
**Evaluate Specific Values**
- **\( f(-1) \)**:
- Evaluate by identifying \( y \) when \( x = -1 \) on the graph.
- **If \( f(x) = 9 \), then \( x = ? \)**:
- Determine whether \( f(x) = 9 \) is possible by checking the graph's maximum point.
**Explanation**
The domain, image, and specific point evaluations help understand the nature and range of possible values for the function \( f(x) \) depicted by the graph.
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