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What is the range of the function [tex]$f(x) = 12 - 3x$[/tex] for the domain [tex]\{-4, -2, 0, 2, 4\}?[/tex]

A. [tex]\{6, 12, 18, 20, 24\}[/tex]
B. [tex]\{6, 12, 18, 24, 30\}[/tex]
C. [tex]\{-12, -6, 0, 6, 12\}[/tex]
D. [tex]\{0, 6, 12, 18, 24\}[/tex]



Answer :

GinnyAnswer
To determine the range of the function [tex]\( f(x) = 12 - 3x \)[/tex] for the given domain [tex]\( \{-4, -2, 0, 2, 4\} \)[/tex], we need to evaluate the function for each value in the domain and find the corresponding value in the range.

1. For [tex]\( x = -4 \)[/tex]:
[tex]\[ f(-4) = 12 - 3(-4) = 12 + 12 = 24 \][/tex]

2. For [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 12 - 3(-2) = 12 + 6 = 18 \][/tex]

3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 12 - 3(0) = 12 \][/tex]

4. For [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 12 - 3(2) = 12 - 6 = 6 \][/tex]

5. For [tex]\( x = 4 \)[/tex]:
[tex]\[ f(4) = 12 - 3(4) = 12 - 12 = 0 \][/tex]

Now we collect all the outputs:
[tex]\[ \{24, 18, 12, 6, 0\} \][/tex]

This collection of values represents the range of the function for the given domain.

Among the provided options, the correct range is:

D. [tex]\(\{0, 6, 12, 18, 24\}\)[/tex]

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