To determine the corresponding range for the function [tex]\(5x + y = 1\)[/tex] given the domain [tex]\(\{-2, 1, 6\}\)[/tex], we need to find the value of [tex]\(y\)[/tex] for each [tex]\(x\)[/tex] in the domain.
First, let's rewrite the given function to express [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex].
[tex]\[ 5x + y = 1 \][/tex]
[tex]\[ y = 1 - 5x \][/tex]
Now, we will evaluate this expression for each value in the domain [tex]\(\{-2, 1, 6\}\)[/tex].
1. For [tex]\(x = -2\)[/tex]:
[tex]\[ y = 1 - 5(-2) \][/tex]
[tex]\[ y = 1 + 10 \][/tex]
[tex]\[ y = 11 \][/tex]
2. For [tex]\(x = 1\)[/tex]:
[tex]\[ y = 1 - 5(1) \][/tex]
[tex]\[ y = 1 - 5 \][/tex]
[tex]\[ y = -4 \][/tex]
3. For [tex]\(x = 6\)[/tex]:
[tex]\[ y = 1 - 5(6) \][/tex]
[tex]\[ y = 1 - 30 \][/tex]
[tex]\[ y = -29 \][/tex]
Thus, the corresponding [tex]\(y\)[/tex]-values are [tex]\(11, -4,\)[/tex] and [tex]\(-29\)[/tex]. Therefore, the range for the domain [tex]\(\{-2, 1, 6\}\)[/tex] is [tex]\(\{11, -4, -29\}\)[/tex].
The correct answer is:
D. [tex]\(\{11, -4, -29\}\)[/tex]
