Question

Which relation is a function?
A. (1, 0), (3, 0), (1, 1), (3, 1) (1, 3)
B. (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
C. (2, 7), (6, 5), (4, 4), (3, 3), (2, 1)
D. (9, −3), (9, 3), (4, −2), (4, 2), (0, 0)

Answer 1

To determine which relation is a function, we need to verify that each input (the first element of each ordered pair) is associated with exactly one output (the second element). If any input is associated with more than one output, it is not a function.

Let's analyze each option:

A. (1, 0), (3, 0), (1, 1), (3, 1), (1, 3)
- The input 1 is associated with outputs 0, 1, and 3 (three different outputs). Therefore, this relation is **not a function**.

B. (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
- Each input (1, 2, 3, 4, and 5) has a unique output (1, 2, 3, 4, and 8 respectively). Therefore, this relation **is a function**.

C. (2, 7), (6, 5), (4, 4), (3, 3), (2, 1)
- The input 2 is associated with outputs 7 and 1 (two different outputs). Therefore, this relation is **not a function**.

D. (9, −3), (9, 3), (4, −2), (4, 2), (0, 0)
- The input 9 is associated with outputs -3 and 3 (two different outputs), and the input 4 is associated with outputs -2 and 2 (two different outputs). Therefore, this relation is **not a function**.

In conclusion, the only relation that is a function is:
**B. (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)**.