To find the range of the function [tex]\( f(x) = -4x - 8 \)[/tex] for the domain [tex]\(\{0, 1, 2\}\)[/tex], we need to evaluate the function at each value within the domain. We'll proceed step-by-step:
1. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = -4(0) - 8 = -8
\][/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]
By applying the function to each value in the domain, we get the corresponding outputs:
- When [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -8 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( f(x) = -12 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( f(x) = -16 \)[/tex]
Thus, the range of the function [tex]\( f(x) = -4x - 8 \)[/tex] for the domain [tex]\(\{0, 1, 2\}\)[/tex] is [tex]\(\{-8, -12, -16\}\)[/tex].
