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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)
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: \([-3, \infty)\)
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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