Question

Which of the following relations are functions?
A. (8, -2), (6, 5), (7, -1), (6, -5)
B. (-1, 3), (-4, 3), (-2, 3), (0, 3)
C. (8, 2), (6, -5), (7, -1), (6, 5)
D. (2, 4) (2, 7), (2, -1), (2, 0)

Answer 1

To determine if a relation is a function, we need to check if every input (the first element of each ordered pair) maps to exactly one output (the second element).

Let's analyze each option:

A. (8, -2), (6, 5), (7, -1), (6, -5)
- The input 6 appears twice: (6, 5) and (6, -5). Since 6 maps to two different outputs, this relation is **not a function**.

B. (-1, 3), (-4, 3), (-2, 3), (0, 3)
- All inputs (-1, -4, -2, 0) are distinct, each mapping to the output 3. This relation is a function.

C. (8, 2), (6, -5), (7, -1), (6, 5)
- The input 6 appears twice: (6, -5) and (6, 5). Since 6 maps to two different outputs, this relation is **not a function**.

D. (2, 4), (2, 7), (2, -1), (2, 0)
- The input 2 appears four times, each time mapping to different outputs (4, 7, -1, 0). Since 2 maps to multiple outputs, this relation is **not a function**.

In summary:
- **A**: Not a function
- **B**: Is a function
- **C**: Not a function
- **D**: Not a function

So, the only relation that is a function is **B**.