To determine the line of reflection between the function $f(x) = x - 2$ and its reflection $g(x) = -2 - x$, let's follow these steps:

Step 1: Find the midpoint between $f(x)$ and $g(x)$

The line of reflection is the line where the distance between a function and its reflection is equal on both sides. This line can be found by averaging the functions.

1. Let $y_1 = f(x) = x - 2$.
2. Let $y_2 = g(x) = -2 - x$.

Step 2: Set the average of the functions to find the line of reflection

The line of reflection will be halfway between $y_1$ and $y_2$.

$\text{Average line} = \frac{y_1 + y_2}{2} = \frac{(x - 2) + (-2 - x)}{2}$

Simplify the equation:

$\text{Average line} = \frac{x - 2 - 2 - x}{2} = \frac{-4}{2} = -2$

Conclusion

The line of reflection is the horizontal line:

$y = -2$

This is the line that equidistantly divides the graphs of the two functions $f(x) = x - 2$ and $g(x) = -2 - x$.

Would you like more details or have any questions?

Here are some related questions to explore:

1. What is the reflection of the function $f(x) = 2x + 1$ across the line $y = -1$?
2. How would you find the line of reflection for two arbitrary functions?
3. What are the properties of a function and its reflection?
4. How can you graphically determine the line of reflection between two functions?
5. What are the implications of reflections on the slope and intercept of a linear function?

Tip: When reflecting a function over a line, visualize how each point on the function mirrors across the line to ensure correct reflection.