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If the function [tex]$5x + y = 1$[/tex] has the domain [tex]\{-2, 1, 6\}[/tex], then what is the corresponding range?

A. [tex]\{-9, 6, 31\}[/tex]

B. [tex]\{9, -6, -31\}[/tex]

C. [tex]\{-11, 4, 29\}[/tex]

D. [tex]\{11, -4, -29\}[/tex]



Answer :

GinnyAnswer
To determine the range of the function [tex]\(5x + y = 1\)[/tex] for a given domain [tex]\(\{-2, 1, 6\}\)[/tex], follow these steps:

1. Rewrite the function in terms of [tex]\(y\)[/tex]:
[tex]\[5x + y = 1 \implies y = 1 - 5x\][/tex]

2. Substitute each value in the domain into [tex]\(y\)[/tex]:
- For [tex]\(x = -2\)[/tex]:
[tex]\[y = 1 - 5(-2) = 1 + 10 = 11\][/tex]

- For [tex]\(x = 1\)[/tex]:
[tex]\[y = 1 - 5(1) = 1 - 5 = -4\][/tex]

- For [tex]\(x = 6\)[/tex]:
[tex]\[y = 1 - 5(6) = 1 - 30 = -29\][/tex]

3. Compile the results:
The corresponding [tex]\(y\)[/tex]-values (range) for the domain [tex]\(\{-2, 1, 6\}\)[/tex] are [tex]\(\{11, -4, -29\}\)[/tex].

Thus, the correct answer is:
[tex]\[ \boxed{D. \{11, -4, -29\}} \][/tex]

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