To find the range given the domain [tex]\(\{-2, 2, 4\}\)[/tex] for the relation defined by the equation [tex]\(3x + y = 3\)[/tex], we will follow these steps:
1. Start with the equation:
[tex]\[
3x + y = 3
\][/tex]
2. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = 3 - 3x
\][/tex]
3. Substitute each value from the domain into the equation to find the corresponding [tex]\(y\)[/tex] values:
- For [tex]\(x = -2\)[/tex]:
[tex]\[
y = 3 - 3(-2) = 3 + 6 = 9
\][/tex]
- For [tex]\(x = 2\)[/tex]:
[tex]\[
y = 3 - 3(2) = 3 - 6 = -3
\][/tex]
- For [tex]\(x = 4\)[/tex]:
[tex]\[
y = 3 - 3(4) = 3 - 12 = -9
\][/tex]
4. Combine the resultant [tex]\(y\)[/tex] values to form the range:
[tex]\[
\{9, -3, -9\}
\][/tex]
Therefore, the correct answer is:
C. [tex]\(\{9, -3, -9\}\)[/tex]
