To solve this problem, we need to find the ordered pairs for the given function [tex]\( f(x) = \frac{3}{2}x + 4 \)[/tex] using the specified domain [tex]\( \{-8, -4, -2, 0, 2, 4\} \)[/tex].
Here’s how you can do it step by step:
1. Evaluate the function at each value of the domain:
- For [tex]\( x = -8 \)[/tex]:
[tex]\[
f(-8) = \frac{3}{2}(-8) + 4 = -12 + 4 = -8
\][/tex]
So, the ordered pair is [tex]\((-8, -8)\)[/tex].
- For [tex]\( x = -4 \)[/tex]:
[tex]\[
f(-4) = \frac{3}{2}(-4) + 4 = -6 + 4 = -2
\][/tex]
So, the ordered pair is [tex]\((-4, -2)\)[/tex].
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
f(-2) = \frac{3}{2}(-2) + 4 = -3 + 4 = 1
\][/tex]
So, the ordered pair is [tex]\((-2, 1)\)[/tex].
- 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].
- For [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = \frac{3}{2}(2) + 4 = 3 + 4 = 7
\][/tex]
So, the ordered pair is [tex]\((2, 7)\)[/tex].
- For [tex]\( x = 4 \)[/tex]:
[tex]\[
f(4) = \frac{3}{2}(4) + 4 = 6 + 4 = 10
\][/tex]
So, the ordered pair is [tex]\((4, 10)\)[/tex].
2. List all the ordered pairs:
[tex]\[
(-8, -8), (-4, -2), (-2, 1), (0, 4), (2, 7), (4, 10)
\][/tex]
3. Plot these ordered pairs on a grid:
To plot the points, follow these steps for each ordered pair [tex]\((x, y)\)[/tex]:
- Start at the origin (0,0).
- Move horizontally to the x-coordinate.
- From there, move vertically to the y-coordinate.
- Mark the point on the grid.
For example:
- For [tex]\((-8, -8)\)[/tex], start at (0,0), move left 8 units to ( -8, 0), then move down 8 units to [tex]\((-8, -8)\)[/tex].
- For [tex]\((-4, -2)\)[/tex], start at (0,0), move left 4 units to [tex]\((-4, 0)\)[/tex], then move down 2 units to [tex]\((-4, -2)\)[/tex].
- Follow similar steps for all other points.
After plotting these points on the grid, you will see the trend of the linear function. If you draw a line through these points, you’ll see that they align straight, confirming the linearity of the function [tex]\( f(x) = \frac{3}{2}x + 4 \)[/tex].
