Math Problem Statement

Determine whether the relation is a function. Give the domain and the range of the relation. ​{(5​,4​),(5​,7​),(7​,4​),(7​,7​)} Question content area bottom Part 1 Is this a​ function?

Solution

A relation is considered a function if each input (the first element in each ordered pair) is associated with exactly one output (the second element in the pair).

Given the relation: {(5,4),(5,7),(7,4),(7,7)}\{(5, 4), (5, 7), (7, 4), (7, 7)\} we can observe that:

  • The input 5 is associated with both 4 and 7.
  • The input 7 is also associated with both 4 and 7.

Since the input 5 corresponds to two different outputs (4 and 7), this relation is not a function.

Domain and Range:

  • Domain: The set of all inputs (first elements): {5,7}\{5, 7\}
  • Range: The set of all outputs (second elements): {4,7}\{4, 7\}

Summary:

  • Is it a function? No.
  • Domain: {5,7}\{5, 7\}
  • Range: {4,7}\{4, 7\}

Would you like further clarification or details on this concept?

Here are five related questions to expand on this information:

  1. What are the key differences between a function and a relation?
  2. How can you graphically determine if a relation is a function?
  3. Can a function have the same output for different inputs?
  4. What is the vertical line test for functions?
  5. What are some examples of real-world functions?

Tip: When checking if a relation is a function, remember that each input must map to exactly one output!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Relations and Functions
Domain and Range

Formulas

-

Theorems

Definition of Function
Vertical Line Test

Suitable Grade Level

Grades 9-11