Math Problem Statement

State whether each relation represents a function based on the mappings provided.

Solution

This image contains a set of mappings for six different relations. The task is to determine whether each relation represents a function. For a relation to be a function, each input (element in the left oval) must be mapped to exactly one output (element in the right oval). No input can have more than one arrow pointing to different outputs.

Analysis:

  1. Relation 1:

    • Each input maps to exactly one output.
    • Conclusion: This is a function.
  2. Relation 2:

    • The input -19 maps to two outputs: -16 and -13.
    • Conclusion: This is not a function.
  3. Relation 3:

    • The input -5 maps to both 10 and 14.
    • Conclusion: This is not a function.
  4. Relation 4:

    • Each input maps to exactly one output.
    • Conclusion: This is a function.
  5. Relation 5:

    • Each input maps to exactly one output.
    • Conclusion: This is a function.
  6. Relation 6:

    • The input 0 maps to both 1 and 4.
    • Conclusion: This is not a function.

Final Results:

  1. Function
  2. Not a function
  3. Not a function
  4. Function
  5. Function
  6. Not a function

Would you like me to explain why certain relations failed to qualify as functions in greater detail?


Related Questions:

  1. What are the defining characteristics of a function in mathematics?
  2. How can we represent functions using sets or tables?
  3. Can a function have duplicate outputs for different inputs?
  4. What are real-world examples of functions and non-functions?
  5. How are functions represented graphically, and what does the vertical line test indicate?

Tip: To confirm if a relation is a function, always check that each input has only one unique output!

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Math Problem Analysis

Mathematical Concepts

Relations and Functions
Mappings

Formulas

-

Theorems

Definition of a Function

Suitable Grade Level

Grades 8-10