**Function Diagram and Range Identification****Sets Definition:**- \( A = \{a, b, c, d\} \)- \( X = \{1, 2, 3, 4\} \)**Function Definition:**The function \( f : A \rightarrow X \) is defined by the arrow diagram below.**Arrow Diagram:**- Element \( a \) is mapped to \( 1 \).- Element \( b \) is mapped to \( 2 \).- Element \( c \) is mapped to \( 2 \).- Element \( d \) is mapped to \( 3 \).**Objective:**Select the set corresponding to the range of \( f \).**Available Options:**- \(\{1, 2, 3, 4\}\)- \(\{2, 3\}\)- \(\{a, b, c, d\}\)**Explanation:**The range of a function is the set of all possible outputs. Based on the arrow diagram, the output values are \(1, 2, \) and \( 3 \). Therefore, the range of \( f \) is \(\{1, 2, 3\}\). The image contains a diagram illustrating a function \( f \) from set \( \{a, b, c, d\} \) to set \( \{1, 2, 3, 4\} \). The function is represented with arrows indicating the mapping of elements from the first set to the second set:- \( a \rightarrow 1 \)- \( b \rightarrow 2 \)- \( c \rightarrow 3 \)- \( d \rightarrow 3 \)Below the diagram, there are multiple-choice options, which seem to ask for a certain property or characteristic related to the sets or function:- \( \) {1, 2, 3, 4}- \( \) {2, 3}- \( \) {a, b, c, d}- \( \) \( \emptyset \) (empty set)This setup is typically used to discuss topics like function range, domain, or image. For instance, it might be exploring the range of the function \( f \).

Answered: Image /qna-images/answer/3d5a454d-3032-4fd5-ae95-2d783e9ed4e9.jpg

Answered: A = {a, b, c, d} X = {1, 2, 3, 4) The…

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 d 4 1 2 3

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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Question

**Function Diagram and Range Identification**

**Sets Definition:**
- \( A = \{a, b, c, d\} \)
- \( X = \{1, 2, 3, 4\} \)

**Function Definition:**
The function \( f : A \rightarrow X \) is defined by the arrow diagram below.

**Arrow Diagram:**
- Element \( a \) is mapped to \( 1 \).
- Element \( b \) is mapped to \( 2 \).
- Element \( c \) is mapped to \( 2 \).
- Element \( d \) is mapped to \( 3 \).

**Objective:**
Select the set corresponding to the range of \( f \).

**Available Options:**
- \(\{1, 2, 3, 4\}\)
- \(\{2, 3\}\)
- \(\{a, b, c, d\}\)

**Explanation:**
The range of a function is the set of all possible outputs. Based on the arrow diagram, the output values are \(1, 2, \) and \( 3 \). Therefore, the range of \( f \) is \(\{1, 2, 3\}\).

The image contains a diagram illustrating a function \( f \) from set \( \{a, b, c, d\} \) to set \( \{1, 2, 3, 4\} \). The function is represented with arrows indicating the mapping of elements from the first set to the second set:

- \( a \rightarrow 1 \)
- \( b \rightarrow 2 \)
- \( c \rightarrow 3 \)
- \( d \rightarrow 3 \)

Below the diagram, there are multiple-choice options, which seem to ask for a certain property or characteristic related to the sets or function:

- \( \) {1, 2, 3, 4}
- \( \) {2, 3}
- \( \) {a, b, c, d}
- \( \) \( \emptyset \) (empty set)

This setup is typically used to discuss topics like function range, domain, or image. For instance, it might be exploring the range of the function \( f \).

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