Question

Which of the following relations is a function?
{9, 3), (6, 3), (0, 3), (9, -3), (7, 3)}
{(-2, 3), (6, 3), (0, 3), (9, 3), (0, -3)}
{(-2, -3), (-2, 3), (0, 3), (9, 3), (7, 3)}
{(-2, 3), (6, 3), (0, 3), (9, 3), (7, 3)}

Answer 1

To determine which of the given relations is a function, we need to check if every input (or first element) maps to exactly one output (or second element). In other words, if any input has more than one output, the relation is not a function.

Let's analyze each relation:

1. **Relation 1:** {(9, 3), (6, 3), (0, 3), (9, -3), (7, 3)}
- Input 9 has two outputs (3 and -3).
- This relation is **not a function**.

2. **Relation 2:** {(-2, 3), (6, 3), (0, 3), (9, 3), (0, -3)}
- Input 0 has two outputs (3 and -3).
- This relation is **not a function**.

3. **Relation 3:** {(-2, -3), (-2, 3), (0, 3), (9, 3), (7, 3)}
- Input -2 has two outputs (-3 and 3).
- This relation is **not a function**.

4. **Relation 4:** {(-2, 3), (6, 3), (0, 3), (9, 3), (7, 3)}
- Each input has a unique output: -2 maps to 3, 6 maps to 3, 0 maps to 3, 9 maps to 3, and 7 maps to 3.
- This relation is a function.

Therefore, **the relation that is a function is:** {(-2, 3), (6, 3), (0, 3), (9, 3), (7, 3)}.