To determine the range of the function [tex]\( y = \frac{1}{2} x + 6 \)[/tex] for the given domain [tex]\(\{6, -8, 4, 2\}\)[/tex], we need to calculate the value of [tex]\( y \)[/tex] for each [tex]\( x \)[/tex] in the domain.
Let's go through each value in the domain step-by-step:
1. For [tex]\( x = 6 \)[/tex]:
[tex]\[
y = \frac{1}{2} \cdot 6 + 6 = 3 + 6 = 9
\][/tex]
2. For [tex]\( x = -8 \)[/tex]:
[tex]\[
y = \frac{1}{2} \cdot (-8) + 6 = -4 + 6 = 2
\][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[
y = \frac{1}{2} \cdot 4 + 6 = 2 + 6 = 8
\][/tex]
4. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = \frac{1}{2} \cdot 2 + 6 = 1 + 6 = 7
\][/tex]
Thus, the range of the function for the given domain [tex]\(\{6, -8, 4, 2\}\)[/tex] is [tex]\(\{9, 2, 8, 7\}\)[/tex].
