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)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**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 \(\{1, 2, 3\}\).
Transcribed Image Text:**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 \( f \).
Transcribed Image Text: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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