Question

Use a mapping diagram to determine whether the relation is a function.
​{(4​,4​), ​(5​,9​), ​(5​,7​), ​(9​,6​), ​(2​,11​), ​(4​,2​)}

Answer 1

To determine whether a relation is a function, we need to check if each input (or x-value) corresponds to exactly one output (or y-value). In other words, no x-value can be associated with more than one y-value.

Let's analyze the given relation:

\[
\{(4,4), (5,9), (5,7), (9,6), (2,11), (4,2)\}
\]

Now, let's isolate the x-values and examine them:

- The x-value 4 appears twice:
- (4, 4)
- (4, 2)

- The x-value 5 also appears twice:
- (5, 9)
- (5, 7)

- The x-values 9 and 2 appear once:
- (9, 6)
- (2, 11)

Since both x-value 4 and x-value 5 have multiple corresponding y-values, this relation does not satisfy the definition of a function.

### Conclusion:
The relation is **not a function** because the x-values 4 and 5 are associated with more than one y-value.