Determine whether the relation is a​ function, and give the domain and range.

20 to 14
14 to 25
13 to 14

1 answer

To determine if the given relation is a function, we need to check if each input (first number) is associated with exactly one output (second number).

Given the pairs:

  • 20 to 14
  • 14 to 25
  • 13 to 14

Step 1: Check for function property

  • The input 20 is paired with the output 14.
  • The input 14 is paired with the output 25.
  • The input 13 is paired with the output 14.

In this case:

  • The input 20 maps to 14 (this is fine).
  • The input 14 maps to 25 (this is also fine).
  • The input 13 maps to 14.

Each input (20, 14, 13) is associated with a unique output. However, the input 14 has two different outputs (it maps to both 14 and 25). This means that the relation is not a function because one input (14) does not have a unique output.

Step 2: Determine the domain and range

  • Domain: The set of all unique inputs.

    • Inputs: 20, 14, 13
    • Therefore, the domain is {20, 14, 13}.
  • Range: The set of all unique outputs.

    • Outputs: 14, 25
    • Therefore, the range is {14, 25}.

Conclusion:

  • Is it a function? No.
  • Domain: {20, 14, 13}
  • Range: {14, 25}