y 10 8 6 4 2 X -5 5 -24 Amazing work. Find the domain of the function. (Enter your answer using interval notation.) (-∞,3]U[3,∞) Good work. Find the range of the function. (Enter your answer using interval notation.) (∞,0) U (6,∞)
y 10 8 6 4 2 X -5 5 -24 Amazing work. Find the domain of the function. (Enter your answer using interval notation.) (-∞,3]U[3,∞) Good work. Find the range of the function. (Enter your answer using interval notation.) (∞,0) U (6,∞)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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### Understanding Domain and Range of Functions
#### Graph Analysis
The provided graph displays two separate line segments plotted on an xy-plane:
1. The first line segment, which starts at \( (-7, 8) \) and ends at \( (-3, 0) \), and moves in a decreasing trend.
2. The second line segment starts at \( (3, 6) \) and ends moving upwards to the right, exiting the upper part of the graph.
Both line segments include the endpoints at \( (-3, 0) \) and \( (3, 6) \).
#### Given Solutions
1. **Domain of the Function**
- The domain refers to all possible x-values for which the function is defined.
- The correct domain for this function is:
\[
(-\infty, -3] \cup [3, \infty)
\]
- This interval indicates that the function is defined for all x-values less than or equal to \(-3\) and all x-values greater than or equal to 3, reflecting the intervals covered by the line segments.
2. **Range of the Function**
- The range refers to all possible y-values that the function can take.
- The attempted range provided is:
\[
(\infty, 0) \cup (6, \infty)
\]
- However, this suggestion is incorrect. It seems there might be a new valid range covering the y-values from \(-\infty\) to \(0\) and from \(6\) to \(\infty\).
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54a9d33b-c075-4af5-8013-3f49004b10ba%2F2e49a3db-0cf2-4931-ba48-91d1e51195e2%2Fdu5z5m7_processed.png&w=3840&q=75)
Transcribed Image Text:---
### Understanding Domain and Range of Functions
#### Graph Analysis
The provided graph displays two separate line segments plotted on an xy-plane:
1. The first line segment, which starts at \( (-7, 8) \) and ends at \( (-3, 0) \), and moves in a decreasing trend.
2. The second line segment starts at \( (3, 6) \) and ends moving upwards to the right, exiting the upper part of the graph.
Both line segments include the endpoints at \( (-3, 0) \) and \( (3, 6) \).
#### Given Solutions
1. **Domain of the Function**
- The domain refers to all possible x-values for which the function is defined.
- The correct domain for this function is:
\[
(-\infty, -3] \cup [3, \infty)
\]
- This interval indicates that the function is defined for all x-values less than or equal to \(-3\) and all x-values greater than or equal to 3, reflecting the intervals covered by the line segments.
2. **Range of the Function**
- The range refers to all possible y-values that the function can take.
- The attempted range provided is:
\[
(\infty, 0) \cup (6, \infty)
\]
- However, this suggestion is incorrect. It seems there might be a new valid range covering the y-values from \(-\infty\) to \(0\) and from \(6\) to \(\infty\).
---
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