From the image, we are tasked to complete the table for the linear function $f(x) = -\frac{1}{2}x$ and use two ordered pairs to graph it. Here's how to calculate the values step by step:

Function:

$f(x) = -\frac{1}{2}x$

Calculations:

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

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

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

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

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

Completed Table:

Graph:

• Plot the ordered pairs $(-4, 2)$, $(-2, 1)$, $(0, 0)$, $(2, -1)$, and $(4, -2)$.
• Draw a straight line passing through these points since the function is linear.

Would you like me to generate an image of the graph or provide further clarification?

Expansion Questions:

1. Why does the function $f(x) = -\frac{1}{2}x$ produce a straight line graph?
2. How do the slope and y-intercept appear in this specific function?
3. What would change if the function had a positive slope, such as $f(x) = \frac{1}{2}x$?
4. How would the graph shift if a constant term like $+3$ were added to $f(x)$?
5. How do you determine ordered pairs efficiently for graphing?

Tip: Remember, the coefficient of $x$ determines the slope, while any added constant determines the y-intercept.