To determine the range for the relation [tex]\(3x + y = 3\)[/tex] given the domain [tex]\(\{-2, 2, 4\}\)[/tex], we can follow these steps:
1. Start with the relation [tex]\(3x + y = 3\)[/tex]. We need to solve for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex].
2. Rearrange the equation:
[tex]\[
y = 3 - 3x
\][/tex]
3. Substitute each value from the domain [tex]\(\{-2, 2, 4\}\)[/tex] into the equation [tex]\(y = 3 - 3x\)[/tex] to find the corresponding values of [tex]\(y\)[/tex].
- When [tex]\(x = -2\)[/tex]:
[tex]\[
y = 3 - 3(-2) = 3 + 6 = 9
\][/tex]
- When [tex]\(x = 2\)[/tex]:
[tex]\[
y = 3 - 3(2) = 3 - 6 = -3
\][/tex]
- When [tex]\(x = 4\)[/tex]:
[tex]\[
y = 3 - 3(4) = 3 - 12 = -9
\][/tex]
4. Collect the calculated values of [tex]\(y\)[/tex] to form the range:
[tex]\[
\{9, -3, -9\}
\][/tex]
Therefore, the range for the relation [tex]\(3x + y = 3\)[/tex] given the domain [tex]\(\{-2, 2, 4\}\)[/tex] is [tex]\(\{9, -3, -9\}\)[/tex].
The correct answer is:
D. [tex]\(\{9, -3, -9\}\)[/tex]
