Let's find the ordered pairs using the given function [tex]\( f(x) = \frac{3}{2}x + 4 \)[/tex] for each value in the domain [tex]\( \{-8, -4, -2, 0, 2, 4\} \)[/tex].
1. For [tex]\( x = -8 \)[/tex]:
[tex]\[
f(-8) = \frac{3}{2}(-8) + 4 = \frac{3 \times -8}{2} + 4 = -12 + 4 = -8
\][/tex]
So, the ordered pair is [tex]\((-8, -8)\)[/tex].
2. For [tex]\( x = -4 \)[/tex]:
[tex]\[
f(-4) = \frac{3}{2}(-4) + 4 = \frac{3 \times -4}{2} + 4 = -6 + 4 = -2
\][/tex]
So, the ordered pair is [tex]\((-4, -2)\)[/tex].
3. For [tex]\( x = -2 \)[/tex]:
[tex]\[
f(-2) = \frac{3}{2}(-2) + 4 = \frac{3 \times -2}{2} + 4 = -3 + 4 = 1
\][/tex]
So, the ordered pair is [tex]\((-2, 1)\)[/tex].
4. For [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = \frac{3}{2}(0) + 4 = 0 + 4 = 4
\][/tex]
So, the ordered pair is [tex]\((0, 4)\)[/tex].
5. For [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = \frac{3}{2}(2) + 4 = \frac{3 \times 2}{2} + 4 = 3 + 4 = 7
\][/tex]
So, the ordered pair is [tex]\((2, 7)\)[/tex].
6. For [tex]\( x = 4 \)[/tex]:
[tex]\[
f(4) = \frac{3}{2}(4) + 4 = \frac{3 \times 4}{2} + 4 = 6 + 4 = 10
\][/tex]
So, the ordered pair is [tex]\((4, 10)\)[/tex].
Given these calculations, the complete list of ordered pairs for the domain [tex]\(\{-8, -4, -2, 0, 2, 4\}\)[/tex] are:
[tex]\[
\{
(-8, -8),
(-4, -2),
(-2, 1),
(0, 4),
(2, 7),
(4, 10)
\}
\][/tex]
These are the points that we would plot on a graph for the function [tex]\( f(x) = \frac{3}{2}x + 4 \)[/tex].
