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Given the following arrow diagrams for functions from A to B, give a possible rule for the function. a. A 9 12 B 23 27 39 51 b. A (0,1) (4,7). (5,1) (2,6) B 23 26 10

Given the following arrow diagrams for functions from A to B, give a possible rule for the function. a. A 9 12 B 23 27 39 51 b. A (0,1) (4,7). (5,1) (2,6) B 23 26 10

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Transcription and Explanation of Arrow Diagrams for Functions:** The image contains two parts, labeled as (a) and (b), which show arrow diagrams representing functions from set A to set B. Each diagram consists of two ellipses, one labeled 'A' and the other 'B', with arrows indicating mappings from elements in set A to elements in set B. ### Diagram (a): - **Set A**: Contains the elements {5, 6, 9, 12}. - **Set B**: Contains the elements {23, 27, 39, 51}. Each element from set A points to an element in set B: - 5 → 23 - 6 → 27 - 9 → 39 - 12 → 51 **Possible Rule for the Function (a)**: The function maps each element \( x \) in set A to \( 3x + 8 \) in set B. ### Diagram (b): - **Set A**: Contains the ordered pairs {(0,1), (4,7), (5,1), (2,6)}. - **Set B**: Contains the numbers {1, 23, 26, 10}. Each element (pair) from set A points to an element in set B: - (0,1) → 1 - (4,7) → 23 - (5,1) → 26 - (2,6) → 10 **Possible Rule for the Function (b)**: The function might combine the elements of each pair in set A, possibly considering operations like addition or linear combinations, to determine the mapping. For example, \( (x, y) \rightarrow 4x + y \). This explanation and rule identification can assist in understanding how mappings are visually and mathematically represented, which is crucial for learning about functions in mathematics.
Transcribed Image Text:**Transcription and Explanation of Arrow Diagrams for Functions:** The image contains two parts, labeled as (a) and (b), which show arrow diagrams representing functions from set A to set B. Each diagram consists of two ellipses, one labeled 'A' and the other 'B', with arrows indicating mappings from elements in set A to elements in set B. ### Diagram (a): - **Set A**: Contains the elements {5, 6, 9, 12}. - **Set B**: Contains the elements {23, 27, 39, 51}. Each element from set A points to an element in set B: - 5 → 23 - 6 → 27 - 9 → 39 - 12 → 51 **Possible Rule for the Function (a)**: The function maps each element \( x \) in set A to \( 3x + 8 \) in set B. ### Diagram (b): - **Set A**: Contains the ordered pairs {(0,1), (4,7), (5,1), (2,6)}. - **Set B**: Contains the numbers {1, 23, 26, 10}. Each element (pair) from set A points to an element in set B: - (0,1) → 1 - (4,7) → 23 - (5,1) → 26 - (2,6) → 10 **Possible Rule for the Function (b)**: The function might combine the elements of each pair in set A, possibly considering operations like addition or linear combinations, to determine the mapping. For example, \( (x, y) \rightarrow 4x + y \). This explanation and rule identification can assist in understanding how mappings are visually and mathematically represented, which is crucial for learning about functions in mathematics.
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