To determine whether a relation is a function, we need to check if each input (value of $x$) is associated with exactly one output (value of $y$).

Here’s the given table:

$x$	$y$
-12	9
16	6
-6	17
7	0
15	9
19	7

Now let's check:

• $x = -12$ corresponds to $y = 9$
• $x = 16$ corresponds to $y = 6$
• $x = -6$ corresponds to $y = 17$
• $x = 7$ corresponds to $y = 0$
• $x = 15$ corresponds to $y = 9$
• $x = 19$ corresponds to $y = 7$

Each $x$-value in the table is unique and is associated with only one $y$-value. There are no repeated $x$-values with different $y$-values.

Conclusion: Yes, this relation is a function because each input has only one output.

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Would you like a further explanation on how functions work, or do you have any other questions?

Here are some related questions:

1. How do you determine if a graph represents a function?
2. Can a function have more than one output for the same input?
3. What is the difference between a relation and a function?
4. How can you test a set of points to see if it's a function?
5. What are some real-world examples of functions?

Tip: A simple way to check if a relation is a function is to ensure that no $x$-value repeats with a different $y$-value.