Let's determine the correct set of possible values for [tex]\( n = 3 \)[/tex].
When [tex]\( n \)[/tex] is 3, we are looking for all the integer values from [tex]\(-n\)[/tex] to [tex]\(n\)[/tex], inclusive. This means:
1. Calculating the negative bound: [tex]\(-3\)[/tex]
2. Calculating the positive bound: [tex]\(3\)[/tex]
Thus, the set of integers includes all numbers from [tex]\(-3\)[/tex] up to [tex]\(3\)[/tex], inclusive. This set includes every integer in this range without skipping any.
Let's list these integers:
- Starting from [tex]\(-3\)[/tex] and moving towards [tex]\(3\)[/tex],
- We get: [tex]\(-3, -2, -1, 0, 1, 2, 3\)[/tex].
Now, we check the given choices to match this set of integers:
1. [tex]\(0, 1, 2\)[/tex] does not match because it is missing [tex]\(-3, -2, -1\)[/tex] and [tex]\(3\)[/tex].
2. [tex]\(0, 1, 2, 3\)[/tex] does not match because it is missing [tex]\(-3, -2, -1\)[/tex].
3. [tex]\(-2, -1, 0, 1, 2\)[/tex] does not match because it is missing [tex]\(-3\)[/tex] and [tex]\(3\)[/tex].
4. [tex]\(-3, -2, -1, 0, 1, 2, 3\)[/tex] matches exactly.
Therefore, the correct set of possible values for [tex]\( n = 3 \)[/tex] is [tex]\(-3, -2, -1, 0, 1, 2, 3\)[/tex].
So, the choice that represents these values correctly is:
[tex]\[
\boxed{4}
\][/tex]
