Let’s analyze each relation to determine if it is a function. A relation is a function if each input (domain value) maps to exactly one output (range value). If an input has multiple outputs, the relation is not a function.

Relation 1

• Each domain value appears only once and maps to a unique range value.
• Conclusion: This is a function.

Relation 2

• Each domain value appears only once and maps to a unique range value.
• No repeated domain values with different outputs.
• Conclusion: This is a function.

Relation 3

{(5, -4), (5, 4), (4, 5), (4, 6)}

• Here, the domain values are repeated:
  • 5 maps to both -4 and 4.
  • 4 maps to both 5 and 6.
• A single input (5 and 4) has multiple outputs, which violates the definition of a function.
• Conclusion: This is not a function.

Relation 4

{(y, 0), (a, 6), (d, -3), (d, 6)}

• The domain value d appears twice with different outputs (-3 and 6).
• This means one input maps to multiple outputs, so it is not a function.
• Conclusion: This is not a function.

Final Answers:

1. Relation 1: Function
2. Relation 2: Function
3. Relation 3: Not a function
4. Relation 4: Not a function

Let me know if you'd like me to explain any specific part further!

Related Questions

1. What is the formal definition of a function in mathematics?
2. How can you use the vertical line test to check for functions graphically?
3. What is the difference between a relation and a function?
4. Can a function have the same output for different inputs?
5. How do you represent functions as equations or tables?

Tip: If a domain value repeats, always check whether it maps to different outputs. If it does, the relation is not a function.