Question

Determine if the following relations are functions and justify why?

{(1, −2), (−2, 0), (−1, 2), (1, 3)}.

Answer 1

The given set of ordered pairs is not a function because the input value 1 is associated with two different outputs, -2 and 3, which violates the definition of a function.

Step-by-step explanation:

To determine if a set of ordered pairs is a function, each input value (x-coordinate) should map to exactly one output value (y-coordinate). Let's examine the given set of ordered pairs:

• (1, −2),
• (−2, 0),
• (−1, 2),
• (1, 3).

We can see that the number 1 is used as the input for two different outputs, -2 and 3. This violates the definition of a function, which requires each input to have a single unique output. Therefore, the relation given by the set of ordered pairs is not a function.