Question

3.1.19
2 parts -- of 1 point
state the domain and range for the following relation. then determine whether the relation represents a function.

daughter | father
clara -> moh
darby -> hank
jenna -> ben
maire -> rabi
flora -> rabi

part 1 of 2

Explanation:

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<reasoning>

Identify the domain elements

The domain is the set of all input values (the independent variable), which corresponds to the "Daughter" set in this mapping diagram.
\[
\text{Domain} = \{\text{Clara}, \text{Darby}, \text{Jenna}, \text{Maire}, \text{Flora}\}
\]

Identify the range elements

The range is the set of all output values (the dependent variable), which corresponds to the "Father" set pointed to by the arrows.
\[
\text{Range} = \{\text{Moh}, \text{Hank}, \text{Ben}, \text{Rabi}\}
\]

Determine if the relation is a function

A relation is a function if each element in the domain maps to exactly one element in the range.
Looking at the mapping:

• Clara maps to Moh (1 output)
• Darby maps to Hank (1 output)
• Jenna maps to Ben (1 output)
• Maire maps to Rabi (1 output)
• Flora maps to Rabi (1 output)

Since every daughter has exactly one father, each input maps to exactly one output. Thus, the relation represents a function.
</reasoning>

<answer>
Domain: \(\{\text{Clara}, \text{Darby}, \text{Jenna}, \text{Maire}, \text{Flora}\}\)

Range: \(\{\text{Moh}, \text{Hank}, \text{Ben}, \text{Rabi}\}\)

Function Determination: Yes, the relation represents a function because each element in the domain maps to exactly one element in the range.
</answer>

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Answer:

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<reasoning>

Identify the domain elements

The domain is the set of all input values (the independent variable), which corresponds to the "Daughter" set in this mapping diagram.
\[
\text{Domain} = \{\text{Clara}, \text{Darby}, \text{Jenna}, \text{Maire}, \text{Flora}\}
\]

Identify the range elements

The range is the set of all output values (the dependent variable), which corresponds to the "Father" set pointed to by the arrows.
\[
\text{Range} = \{\text{Moh}, \text{Hank}, \text{Ben}, \text{Rabi}\}
\]

Determine if the relation is a function

A relation is a function if each element in the domain maps to exactly one element in the range.
Looking at the mapping:

• Clara maps to Moh (1 output)
• Darby maps to Hank (1 output)
• Jenna maps to Ben (1 output)
• Maire maps to Rabi (1 output)
• Flora maps to Rabi (1 output)

Since every daughter has exactly one father, each input maps to exactly one output. Thus, the relation represents a function.
</reasoning>

<answer>
Domain: \(\{\text{Clara}, \text{Darby}, \text{Jenna}, \text{Maire}, \text{Flora}\}\)

Range: \(\{\text{Moh}, \text{Hank}, \text{Ben}, \text{Rabi}\}\)

Function Determination: Yes, the relation represents a function because each element in the domain maps to exactly one element in the range.
</answer>

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