To determine which of the given relations is a function, we need to verify that for each input value (x), there is only one corresponding output value (y). This means that no input value (x) should map to more than one output value (y).
Let's examine each relation one by one:
1. [tex]\(\{(0,0),(0,1),(2,3),(4,5)\}\)[/tex]
- Input 0 maps to both 0 and 1. (Violation of the definition of a function)
- Therefore, this relation is not a function.
2. [tex]\(\{(-4,3),(-4,2),(1,9),(6,7)\}\)[/tex]
- Input -4 maps to both 3 and 2. (Violation of the definition of a function)
- Therefore, this relation is not a function.
3. [tex]\(\{(2,1),(4,2),(2,3),(8,4)\}\)[/tex]
- Input 2 maps to both 1 and 3. (Violation of the definition of a function)
- Therefore, this relation is not a function.
4. [tex]\(\{(-4,3),(-2,0),(2,7),(3,9)\}\)[/tex]
- Each input maps to exactly one output:
- -4 maps to 3
- -2 maps to 0
- 2 maps to 7
- 3 maps to 9
- Therefore, this relation is a function.
By examining each relation, we conclude that the only relation that satisfies the definition of a function is:
[tex]\(\{(-4,3),(-2,0),(2,7),(3,9)\}\)[/tex].
So, the relation that is a function is:
4. [tex]\(\{(-4,3),(-2,0),(2,7),(3,9)\}\)[/tex]
