To find the linear function $f(x)$, we need to determine the equation of the line that passes through the points $(-4, -2)$, $(0, -2)$, and $(-1, 0)$.

Step 1: Use two points to find the slope

We can calculate the slope $m$ using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

We'll use the points $(-4, -2)$ and $(0, -2)$.

$m = \frac{-2 - (-2)}{0 - (-4)} = \frac{0}{4} = 0$

So, the slope of the line is $m = 0$.

Step 2: Use the slope and one point to write the equation

Since the slope is $0$, this tells us the function is a horizontal line. The equation of a horizontal line is simply $y = c$, where $c$ is the constant value of $f(x)$.

Looking at any of the points (e.g., $(0, -2)$), we see that $f(x) = -2$.

Final Answer:

$f(x) = -2$

Would you like more details, or do you have any other questions?

Here are some related questions to expand on this:

1. How can you find the slope of a line passing through two points?
2. What is the general form of a linear equation?
3. How do you find the equation of a line if given two points?
4. How do you recognize if a line is horizontal or vertical from a set of points?
5. How would you find the equation of a vertical line?

Tip: Always double-check your points to make sure they are correct when calculating the slope or equation of a line!