Use the graph of the relation to identify the domain and range. y=xl-3 19 Ay OA. domain: (-00, 00) range: (-3, ∞o) OB. domain: (-00,00) range: (-∞0, ∞0) OC. domain: (-∞0,00) range: (-3, 3) O D. domain: (-00,00) range: [-3, co)
Use the graph of the relation to identify the domain and range. y=xl-3 19 Ay OA. domain: (-00, 00) range: (-3, ∞o) OB. domain: (-00,00) range: (-∞0, ∞0) OC. domain: (-∞0,00) range: (-3, 3) O D. domain: (-00,00) range: [-3, co)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Title:** Understanding Domain and Range from Graphs
**Introduction:**
Use the graph of the relation to identify the domain and range.
**Function:**
\[ y = |x| - 3 \]
**Graph Description:**
The graph is a V-shaped graph of the absolute value function \( y = |x| - 3 \). The vertex of the graph is at the point (0, -3) on the coordinate plane. The graph opens upwards.
- **X-axis:** The graph extends infinitely in both the positive and negative x-directions.
- **Y-axis:** The graph starts at -3 and extends upwards to infinity.
**Options for Domain and Range:**
- **A.**
- Domain: \((-\infty, \infty)\)
- Range: \((-3, \infty)\)
- **B.**
- Domain: \((-\infty, \infty)\)
- Range: \((-\infty, \infty)\)
- **C.**
- Domain: \((-\infty, \infty)\)
- Range: \((-3, 3)\)
- **D.**
- Domain: \((-\infty, \infty)\)
- Range: \([-3, \infty)\)
**Explanation:**
The domain of the function, represented by the graph, includes all real numbers since the graph extends infinitely in both the positive and negative x-directions. Therefore, the domain is \((-\infty, \infty)\).
The range of the function starts at \(y = -3\) and extends upwards to infinity. The lower bound is -3, which forms part of the range. Hence, the correct range is \([-3, \infty)\).
**Correct Option:**
- **D.**
- Domain: \((-\infty, \infty)\)
- Range: \([-3, \infty)\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7aaef1cc-8a78-4690-93ba-afad066da5ab%2F658790e6-1c81-462b-8e2b-3fb356776676%2Fjrvute8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title:** Understanding Domain and Range from Graphs
**Introduction:**
Use the graph of the relation to identify the domain and range.
**Function:**
\[ y = |x| - 3 \]
**Graph Description:**
The graph is a V-shaped graph of the absolute value function \( y = |x| - 3 \). The vertex of the graph is at the point (0, -3) on the coordinate plane. The graph opens upwards.
- **X-axis:** The graph extends infinitely in both the positive and negative x-directions.
- **Y-axis:** The graph starts at -3 and extends upwards to infinity.
**Options for Domain and Range:**
- **A.**
- Domain: \((-\infty, \infty)\)
- Range: \((-3, \infty)\)
- **B.**
- Domain: \((-\infty, \infty)\)
- Range: \((-\infty, \infty)\)
- **C.**
- Domain: \((-\infty, \infty)\)
- Range: \((-3, 3)\)
- **D.**
- Domain: \((-\infty, \infty)\)
- Range: \([-3, \infty)\)
**Explanation:**
The domain of the function, represented by the graph, includes all real numbers since the graph extends infinitely in both the positive and negative x-directions. Therefore, the domain is \((-\infty, \infty)\).
The range of the function starts at \(y = -3\) and extends upwards to infinity. The lower bound is -3, which forms part of the range. Hence, the correct range is \([-3, \infty)\).
**Correct Option:**
- **D.**
- Domain: \((-\infty, \infty)\)
- Range: \([-3, \infty)\)
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