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27 May, 07:25

Which relation defined by a set of ordered pairs is a function?

1. { (6, 2), (6, 3), (5, 4), (6, 6), (7, 6) }

2. { (2, 6), (3, 6), (4, 5), (6, 6), (7, 6) }

3. { (-2, 6), (3, - 6), (-4, 5), (6, - 6), (6, - 7) }

4. { (2, 6), (3, 6), (4, 5), (6, 6), (6, 7) }

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Answers (1)
  1. 27 May, 11:19
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    The relation { (2, 6), (3, 6), (4, 5), (6, 6), (7, 6) } is a function ⇒ answer 2

    Step-by-step explanation:

    - Relation is a set of inputs and outputs

    - Function is a relation where each input has only one output

    - Ex: The relation { (2, 3), (2, 5), (3, 7) } is not a function because the

    input 2 has two outputs 3 and 5

    The relation { (-2, 3), (2, 5), (3, 7) } is a function because each input

    has only one output

    * Let us solve the problem

    - The first relation is:

    { (6, 2), (6, 3), (5, 4), (6, 6), (7, 6) }

    ∵ The input 6 has three outputs 2, 3, 6

    ∴ The relation is not a function

    - The second relation is:

    { (2, 6), (3, 6), (4, 5), (6, 6), (7, 6) }

    ∵ Each input has only one output

    ∴ The relation is a function

    - The third relation is:

    { (-2, 6), (3, - 6), (-4, 5), (6, - 6), (6, - 7) }

    ∵ The input 6 has two outputs - 6, - 7

    ∴ The relation is not a function

    - The fourth relation is:

    { (2, 6), (3, 6), (4, 5), (6, 6), (6, 7) }

    ∵ The input 6 has two outputs 6, 7

    ∴ The relation is not a function

    * The relation { (2, 6), (3, 6), (4, 5), (6, 6), (7, 6) } is a function
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