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A = (a, b, c, d} X = {1,2,3,4} The function f: A→ X is defined by the arrow diagram below. Select the set corresponding to the range of f. a b C d O 1 {1, 2, 3, 4) {2,3} {a, b, c, d} Ø 2 3 ● 4

A = (a, b, c, d} X = {1,2,3,4} The function f: A→ X is defined by the arrow diagram below. Select the set corresponding to the range of f. a b C d O 1 {1, 2, 3, 4) {2,3} {a, b, c, d} Ø 2 3 ● 4

Advanced Engineering Mathematics
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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Discrete Math
**Transcription for Educational Website** **Sets and Functions: Understanding Range with Arrow Diagrams** **Given Sets:** - \( A = \{ a, b, c, d \} \) - \( X = \{ 1, 2, 3, 4 \} \) **Function Description:** The function \( f : A \to X \) is defined by the arrow diagram below. Our goal is to determine the range of the function \( f \). **Arrow Diagram Explanation:** In the diagram, elements from set \( A \) are mapped to elements in set \( X \): - \( a \) maps to \( 1 \) - \( b \) maps to \( 2 \) - \( c \) maps to \( 2 \) - \( d \) maps to \( 3 \) **Task:** Select the set corresponding to the range of \( f \). **Choices:** - \( \{ 1, 2, 3, 4 \} \) - \( \{ 2, 3 \} \) - \( \{ a, b, c, d \} \) - \( \emptyset \) **Explanation:** The range of a function is the set of all images of elements in the domain. From the arrow diagram, the elements in \( X \) that have incoming arrows are \( 1, 2, \) and \( 3 \). Therefore, the range of \( f \) is \( \{ 1, 2, 3 \} \). However, based on the options given, the closest correct choice is not available, leading us to assume a possible mislisting in the options, since the correct response is likely intended to be \( \{ 1, 2, 3 \} \). **Correct Selection:** The correct intended selection for the range, based on diagram analysis, should be \( \{ 1, 2, 3 \} \).
Transcribed Image Text:**Transcription for Educational Website** **Sets and Functions: Understanding Range with Arrow Diagrams** **Given Sets:** - \( A = \{ a, b, c, d \} \) - \( X = \{ 1, 2, 3, 4 \} \) **Function Description:** The function \( f : A \to X \) is defined by the arrow diagram below. Our goal is to determine the range of the function \( f \). **Arrow Diagram Explanation:** In the diagram, elements from set \( A \) are mapped to elements in set \( X \): - \( a \) maps to \( 1 \) - \( b \) maps to \( 2 \) - \( c \) maps to \( 2 \) - \( d \) maps to \( 3 \) **Task:** Select the set corresponding to the range of \( f \). **Choices:** - \( \{ 1, 2, 3, 4 \} \) - \( \{ 2, 3 \} \) - \( \{ a, b, c, d \} \) - \( \emptyset \) **Explanation:** The range of a function is the set of all images of elements in the domain. From the arrow diagram, the elements in \( X \) that have incoming arrows are \( 1, 2, \) and \( 3 \). Therefore, the range of \( f \) is \( \{ 1, 2, 3 \} \). However, based on the options given, the closest correct choice is not available, leading us to assume a possible mislisting in the options, since the correct response is likely intended to be \( \{ 1, 2, 3 \} \). **Correct Selection:** The correct intended selection for the range, based on diagram analysis, should be \( \{ 1, 2, 3 \} \).
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