Math Problem Statement
Solution
In the given relation, we have two sets: Daughter and Letter. The relation connects daughters to letters as follows:
- Clara → Mark
- Darby → Hank
- Jenna → Ben
- Marie → Rubi
- Fiona → Ben
Domain and Range:
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Domain: The set of all inputs (daughters):
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Range: The set of all outputs (letters):
Is this a Function?
A relation is a function if each input (element of the domain) maps to exactly one output (element of the range). Here:
- Clara, Darby, Jenna, and Marie each have exactly one letter associated with them.
- Fiona and Jenna both map to Ben, but this is allowed since each input (daughter) still maps to only one output (letter).
Thus, yes, this relation represents a function because each daughter is associated with only one letter.
Would you like more details or further explanations on any part? Here are five related questions to deepen your understanding:
- What is the difference between a relation and a function?
- Can a function have repeated elements in its range?
- What would happen if one daughter mapped to two different letters?
- How can you visually identify a function from a mapping diagram?
- What are examples of real-life scenarios where functions are used?
Tip: Always check if each input has a unique output to determine if a relation is a function.
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Domain and Range
Formulas
-
Theorems
Definition of a function: each input maps to exactly one output
Suitable Grade Level
Grades 8-10
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