Which relation is a function?

Question

Responses

{(4, 2), (3, 3), (2,  4), (3, 2)}
left bracket ordered pair 4 comma 2 end ordered pair comma ordered pair 3 comma 3 end ordered pair comma ordered pair 2 comma 4 end ordered pair comma ordered pair 3 comma 2 end ordered pair right bracket

{(1, −1), (−2, 2), (−1,  2), (1, −2)}
left bracket begin ordered pair 1 comma negative 1 end ordered pair, begin ordered pair negative 2 comma 2 end ordered pair, begin ordered pair negative comma 2 end ordered pair, begin ordered pair 1 comma negative 2 end ordered pair

{(1, 4), (2, 3), (3,  2), (4, 1)}
left bracket begin ordered pair 1 comma 4 end ordered pair comma begin ordered pair 2 comma 3 end ordered pair comma begin ordered pair 3 comma 2 end ordered pair comma begin ordered pair 4 comma 1 end ordered pair right bracket

{(1, 2), (2, 3), (3,  2), (2, 1)}​
left bracket ordered pair 1 comma 2 end ordered pair comma ordered pair 2 comma 3 end ordered pair comma ordered pair 3 comma 2 end ordered pair ordered pair 2 comma 1 end ordered pair right bracket ​

Answer 1

To determine which of the given relations is a function, we need to check if each input (the first element of the ordered pair) corresponds to exactly one output (the second element of the ordered pair). In other words, for a relation to be a function, there should be no two ordered pairs with the same first element and different second elements.

Let's evaluate each relation:

1. Relation 1: \({(4, 2), (3, 3), (2, 4), (3, 2)}\)

   • Here, the input "3" corresponds to two different outputs (3 and 2).
   • Not a function.

2. Relation 2: \({(1, -1), (-2, 2), (-1, 2), (1, -2)}\)

   • The input "1" corresponds to two different outputs (-1 and -2).
   • Not a function.

3. Relation 3: \({(1, 4), (2, 3), (3, 2), (4, 1)}\)

   • Each input (1, 2, 3, and 4) has a unique output.
   • This is a function.

4. Relation 4: \({(1, 2), (2, 3), (3, 2), (2, 1)}\)

   • The input "2" corresponds to two different outputs (3 and 1).
   • Not a function.

Based on the evaluations, the relation that is a function is:

Relation 3: \({(1, 4), (2, 3), (3, 2), (4, 1)}\)