Question

Choose if the following relations are functions or not functions.

{(1, 3), (2, 3), (-8, 3), (0, 3)} is ___

{(4, 9), (-3, 1), (6, 3), (4, 3), (7, 14)} is ___

{(3, 2.5), (8, -1.4), (4.5, -10), (3, 2.5), (1.2, 1.8)} is ___

{(0, 0), (-1, 1), (-2, 2), (-3, 3), (-4, 4)} is ___

Answer 1

To determine whether each of the given relations is a function or not, we need to check if every input (or first element of each ordered pair) is associated with exactly one output (or second element). In other words, no two ordered pairs can have the same first element with different second elements.

1. **{(1, 3), (2, 3), (-8, 3), (0, 3)}** is **a function**.
Each input (1, 2, -8, 0) is unique, and they all map to the same output (3).

2. **{(4, 9), (-3, 1), (6, 3), (4, 3), (7, 14)}** is **not a function**.
The input 4 is associated with two different outputs (9 and 3).

3. **{(3, 2.5), (8, -1.4), (4.5, -10), (3, 2.5), (1.2, 1.8)}** is **not a function**.
The input 3 appears twice, leading to the same output (2.5), which does not violate the function definition, but the presence of duplicate pairs does not affect the function status.

4. **{(0, 0), (-1, 1), (-2, 2), (-3, 3), (-4, 4)}** is **a function**.
Each input (0, -1, -2, -3, -4) is unique and maps to exactly one output.

In summary:
1. Function
2. Not a function
3. Not a function
4. Function