Math Problem Statement

State the domain and range for the given relation, then determine whether the relation represents a function.

Solution

In the given relation, we have two sets: Daughter and Letter. The relation connects daughters to letters as follows:

  • ClaraMark
  • DarbyHank
  • JennaBen
  • MarieRubi
  • FionaBen

Domain and Range:

  • Domain: The set of all inputs (daughters): {Clara, Darby, Jenna, Marie, Fiona}\{ \text{Clara, Darby, Jenna, Marie, Fiona} \}

  • Range: The set of all outputs (letters): {Mark, Hank, Ben, Rubi}\{ \text{Mark, Hank, Ben, Rubi} \}

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:

  1. What is the difference between a relation and a function?
  2. Can a function have repeated elements in its range?
  3. What would happen if one daughter mapped to two different letters?
  4. How can you visually identify a function from a mapping diagram?
  5. 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