Let's analyze each relation to determine if it's a function.

Relation 1:

• A function must assign each element in the domain to exactly one element in the range.
• In this case, the domain has "lake," "paper," "leaf," and "tree," each mapped to only one unique value in the range.
  • "lake" → 4
  • "paper" → 4
  • "leaf" → -6
  • "tree" → -6
• No domain element is paired with more than one range element, so Relation 1 is a function.

Relation 2:

• In this relation, some elements of the domain have more than one output:
  • 4 → 8 and 4 → -1
  • 9 → -1 and 9 → 6
• Since a function cannot assign more than one output to the same input, Relation 2 is not a function.

Relation 3:

• This is written as a set of ordered pairs: $(b, x), (b, t), (b, b), (b, n)$.
• The domain element "b" is paired with multiple different range elements (x, t, b, n), which violates the rule that each input must have exactly one output.
• Therefore, Relation 3 is not a function.

Relation 4:

• The pairs are $(-5, e), (-7, k), (1, r), (-9, v)$.
• Each input is mapped to exactly one output, with no repetitions in the domain.
• Therefore, Relation 4 is a function.

Summary:

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

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What conditions must a relation satisfy to be classified as a function?
2. Can a function have multiple elements in the range mapped to the same domain element?
3. How can we visually identify functions using a mapping diagram?
4. What is the difference between injective and surjective functions?
5. How can we determine if a relation is a function from its graph?

Tip: To check if a relation is a function, remember the vertical line test for graphs or check if any input is paired with more than one output.