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Given the domain [tex]\(\{-4, 0, 5\}\)[/tex], what is the range for the relation [tex]\(12x + 6y = 24\)[/tex]?

A. [tex]\(\{12, 4, -6\}\)[/tex]
B. [tex]\(\{-4, 4, 14\}\)[/tex]
C. [tex]\(\{-12, -4, 6\}\)[/tex]
D. [tex]\(\{2, 4, 9\}\)[/tex]

Sagot :

GinnyAnswer
To find the range of the relation [tex]\( 12x + 6y = 24 \)[/tex] given the domain [tex]\(\{-4, 0, 5\}\)[/tex], we need to find the corresponding [tex]\( y \)[/tex] values for each [tex]\( x \)[/tex] in the domain.

The relation is:

[tex]\[12x + 6y = 24\][/tex]

First, solve for [tex]\( y \)[/tex]:

[tex]\[12x + 6y = 24 \rightarrow 6y = 24 - 12x \rightarrow y = \frac{24 - 12x}{6} \rightarrow y = 4 - 2x\][/tex]

Now, we will calculate [tex]\( y \)[/tex] for each [tex]\( x \)[/tex] in the domain [tex]\(\{-4, 0, 5\}\)[/tex]:

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

[tex]\[ y = 4 - 2(-4) \][/tex]
[tex]\[ y = 4 + 8 \][/tex]
[tex]\[ y = 12 \][/tex]

2. For [tex]\( x = 0 \)[/tex]:

[tex]\[ y = 4 - 2(0) \][/tex]
[tex]\[ y = 4 \][/tex]

3. For [tex]\( x = 5 \)[/tex]:

[tex]\[ y = 4 - 2(5) \][/tex]
[tex]\[ y = 4 - 10 \][/tex]
[tex]\[ y = -6 \][/tex]

Thus, the range for the given domain is [tex]\(\{12, 4, -6\}\)[/tex].

Therefore, the correct answer is:

A. [tex]\(\{12, 4, -6\}\)[/tex]
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