Math Problem Statement

Determine if the relation is a function: {(1, 2), (3, 4), (1, 5)}

Solution

To determine if a given relation is a function, we need to verify if each input (or first element of the ordered pairs) maps to exactly one output (or second element). In other words, no input can be paired with more than one output.

The given relation is: {(1,2),(3,4),(1,5)}\{(1, 2), (3, 4), (1, 5)\}

  • The input 11 is paired with both 22 and 55.
  • The input 33 is paired with 44.

Since the input 11 is associated with two different outputs (22 and 55), this relation is not a function. In a function, an input can only be associated with one output.

Would you like more details or have any questions about this? Here are five related questions to expand on this concept:

  1. What is the formal definition of a function?
  2. How can we represent functions using function notation?
  3. How do you determine the domain and range of a function?
  4. Can a relation with the same outputs but different inputs be a function?
  5. What is the difference between one-to-one functions and general functions?

Tip: In a function, each input must have exactly one corresponding output, but multiple inputs can share the same output.

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Math Problem Analysis

Mathematical Concepts

Relations and Functions
Set Theory
Ordered Pairs

Formulas

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Theorems

Definition of a Function

Suitable Grade Level

Grades 8-10