Question

Domain, Range

4, -> 1
3, -> 1
2, -> 4
1, -> 4

Based on the mapping diagram of the relation, determine which of the following options is accurate

Option 1 the relation is a function

Option 2 the relation is not a function

Answer 1

In a function, each input (or domain element) must map to exactly one output (or range element).

In the relation provided:

- For input 4, the output is 1.
- For input 3, the output is 1.
- For input 2, the output is 4.
- For input 1, the output is 4.

Here, the inputs 2 and 1 both map to the output 4, which is allowed. However, the main criterion for a function is that no input should map to more than one output.

In this case, each input maps to a single output:

- Inputs 4 and 3 map to different outputs.
- Inputs 2 and 1 also map to different outputs.

Since each input maps to one output and no input shares different outputs, we can conclude that this relation **is not** a function.

Therefore, the correct option is:

**Option 2: the relation is not a function.**