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If the function [tex]\(5x + y = 1\)[/tex] has the domain [tex]\(\{-2, 1, 6\}\)[/tex], 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]

Sagot :

GinnyAnsweridn
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]
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