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Select Is a Function or Is not a Function to correctly classify each relation.

Is a Function Is not a Function
{(3, 7),(3, 6),(5, 4),(4, 7)}

{(1, 5),(3, 5),(4, 6),(6, 4)}

{(2, 3),(4, 2),(4, 6),(5, 8)}

{(0, 4),(3, 2),(4, 2),(6, 5)}

1 answer

To determine if a relation is a function, we need to check if each input (first element of the ordered pair) is associated with exactly one output (second element). If any input is paired with multiple outputs, it is not a function.

Let's classify the given relations:

  1. {(3, 7),(3, 6),(5, 4),(4, 7)}

    • This relation has the input "3" associated with two different outputs (7 and 6).
      Is not a Function

  2. {(1, 5),(3, 5),(4, 6),(6, 4)}

    • Each input (1, 3, 4, and 6) is associated with only one output.
      Is a Function

  3. {(2, 3),(4, 2),(4, 6),(5, 8)}

    • The input "4" is associated with two different outputs (2 and 6).
      Is not a Function

  4. {(0, 4),(3, 2),(4, 2),(6, 5)}

    • Each input (0, 3, 4, and 6) is associated with only one output.
      Is a Function

Now, compiling the classifications:

| Relation | Classification | |:-------------------------------------------------:|:-----------------------:| | {(3, 7),(3, 6),(5, 4),(4, 7)} | Is not a Function | | {(1, 5),(3, 5),(4, 6),(6, 4)} | Is a Function | | {(2, 3),(4, 2),(4, 6),(5, 8)} | Is not a Function | | {(0, 4),(3, 2),(4, 2),(6, 5)} | Is a Function |