Answer :
Absolutely, let's look at whether each of the relations represented by the sets of ordered pairs can be classified as functions. For a relation to be a function, each input (or first element of the ordered pair) must map to exactly one output (or second element of the ordered pair). This means no input value (first component) can repeat with different output values (second component).
Let's analyze each relation one by one.
#### First Relation:
[tex]\[ \{(4,9),(0,-2),(0,2),(5,4)\} \][/tex]
- Ordered Pair Analysis:
- 4 maps to 9
- 0 maps to -2
- 0 maps to 2
- 5 maps to 4
Here, the input 0 is associated with two different outputs: -2 and 2. This violates the definition of a function. Therefore, this relation is not a function.
#### Second Relation:
[tex]\[ \{(5,-5),(5,-4),(7,-2),(3,8)\} \][/tex]
- Ordered Pair Analysis:
- 5 maps to -5
- 5 maps to -4
- 7 maps to -2
- 3 maps to 8
In this relation, the input 5 is associated with two different outputs: -5 and -4. This also violates the definition of a function. Therefore, this relation is not a function.
#### Third Relation:
[tex]\[ \{(4,3),(8,0),(5,2),(-5,0)\} \][/tex]
- Ordered Pair Analysis:
- 4 maps to 3
- 8 maps to 0
- 5 maps to 2
- -5 maps to 0
In this relation, each input value maps to exactly one unique output value, and no input value is repeated. Therefore, this relation satisfies the definition of a function.
### Conclusion:
Only the third relation:
[tex]\[ \{(4,3),(8,0),(5,2),(-5,0)\} \][/tex]
represents a function.
So the correct answer is:
[tex]\(\{(4,3),(8,0),(5,2),(-5,0)\}\)[/tex]
Let's analyze each relation one by one.
#### First Relation:
[tex]\[ \{(4,9),(0,-2),(0,2),(5,4)\} \][/tex]
- Ordered Pair Analysis:
- 4 maps to 9
- 0 maps to -2
- 0 maps to 2
- 5 maps to 4
Here, the input 0 is associated with two different outputs: -2 and 2. This violates the definition of a function. Therefore, this relation is not a function.
#### Second Relation:
[tex]\[ \{(5,-5),(5,-4),(7,-2),(3,8)\} \][/tex]
- Ordered Pair Analysis:
- 5 maps to -5
- 5 maps to -4
- 7 maps to -2
- 3 maps to 8
In this relation, the input 5 is associated with two different outputs: -5 and -4. This also violates the definition of a function. Therefore, this relation is not a function.
#### Third Relation:
[tex]\[ \{(4,3),(8,0),(5,2),(-5,0)\} \][/tex]
- Ordered Pair Analysis:
- 4 maps to 3
- 8 maps to 0
- 5 maps to 2
- -5 maps to 0
In this relation, each input value maps to exactly one unique output value, and no input value is repeated. Therefore, this relation satisfies the definition of a function.
### Conclusion:
Only the third relation:
[tex]\[ \{(4,3),(8,0),(5,2),(-5,0)\} \][/tex]
represents a function.
So the correct answer is:
[tex]\(\{(4,3),(8,0),(5,2),(-5,0)\}\)[/tex]
