To find the range of the function [tex]\( f(x) = -4x - 8 \)[/tex] for the given domain [tex]\(\{0, 1, 2\}\)[/tex], we will evaluate the function at each value in the domain.
1. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = -4(0) - 8 = 0 - 8 = -8
\][/tex]
2. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 1 \)[/tex]:
[tex]\[
f(1) = -4(1) - 8 = -4 - 8 = -12
\][/tex]
3. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = -4(2) - 8 = -8 - 8 = -16
\][/tex]
The range of the function for the domain [tex]\(\{0, 1, 2\}\)[/tex] is therefore the set of outputs obtained from these evaluations. Hence, the range is:
[tex]\[
\boxed{[-8, -12, -16]}
\][/tex]
