Let's analyze these relations to determine whether they represent functions.

Question 7: $(3, 2), (1, 2), (4, 3), (6, -2)$

• A relation is a function if each input (x-value) corresponds to exactly one output (y-value).
• The inputs (x-values) here are: $3, 1, 4, 6$.
• All these x-values are unique, meaning no input is repeated.

Conclusion for 7: Yes, this relation is a function.

Question 8: $(-1, -1), (-2, -2), (-3, 2), (-2, 3)$

• Let's list the inputs (x-values): $-1, -2, -3, -2$.
• Notice that the input $-2$ is repeated, but with two different outputs: $-2$ and $3$.
• Since one input leads to two different outputs, this relation is not a function.

Conclusion for 8: No, this relation is not a function.

Would you like more details about functions or need help with further concepts?

Here are 5 related questions:

1. What is the difference between a relation and a function?
2. How do you determine if a graph represents a function?
3. What is the vertical line test for functions?
4. Can a function have repeated outputs (y-values)?
5. How do domain and range relate to functions?

Tip: A function assigns each input exactly one output, but outputs (y-values) can be repeated.