This problem asks you to complete a table for the function $f(x) = \frac{1}{2}x - 1$, then use the ordered pairs to graph the function. Let’s calculate the values of $f(x)$ for the given $x$-values:

Step-by-step calculations:

1. For $x = -8$: $f(x) = \frac{1}{2}(-8) - 1 = -4 - 1 = -5$ Ordered pair: $(-8, -5)$

2. For $x = -4$: $f(x) = \frac{1}{2}(-4) - 1 = -2 - 1 = -3$ Ordered pair: $(-4, -3)$

3. For $x = 0$: $f(x) = \frac{1}{2}(0) - 1 = 0 - 1 = -1$ Ordered pair: $(0, -1)$

4. For $x = 4$: $f(x) = \frac{1}{2}(4) - 1 = 2 - 1 = 1$ Ordered pair: $(4, 1)$

5. For $x = 8$: $f(x) = \frac{1}{2}(8) - 1 = 4 - 1 = 3$ Ordered pair: $(8, 3)$

Completed Table:

Graph:

Plot these points on the graph: $(-8, -5), (-4, -3), (0, -1), (4, 1), (8, 3)$. Connect them with a straight line, as this is a linear function.

Would you like me to create a graph or clarify any part? Let me know!

Related Questions:

1. What does the slope ($\frac{1}{2}$) of the function represent?
2. How would the graph change if the equation was $f(x) = \frac{1}{2}x + 1$?
3. What is the y-intercept of the function, and why?
4. Can you calculate $f(x)$ for $x = -2$ and add it to the table?
5. How do we know this is a linear function?

Tip: For linear functions, the slope ($m$) determines how much $y$ changes for every unit change in $x$.