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Given the domain [tex]\{-2,2,4\}[/tex], what is the range for the relation [tex]3x + y = 3[/tex]?
A. [tex]\{-9, 3, 9\}[/tex] B. [tex]\{-3, 9, 15\}[/tex] C. [tex]\{0, 5, 7\}[/tex] D. [tex]\{9, -3, -9\}[/tex]
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].
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