Use the *r* notation to write the rule for transforming from f(x) to g(x).

To express the transformation from \( f(x) = x - 2 \) to \( g(x) = -2 - x \) using the \( r \) notation, we need to determine how \( f(x) \) is transformed into \( g(x) \).

The \( r \) notation typically describes reflections, rotations, translations, or scaling of functions. For reflections, we use the form \( r_{y=c} \) to reflect over a horizontal line \( y = c \), and \( r_{x=d} \) to reflect over a vertical line \( x = d \).

Since we found that the line of reflection is \( y = -2 \), the rule for the transformation is a reflection over this line.

### Transformation Rule Using \( r \) Notation

The transformation from \( f(x) \) to \( g(x) \) can be written as:

\[
g(x) = r_{y=-2}(f(x))
\]

This notation indicates that \( g(x) \) is obtained by reflecting \( f(x) \) over the line \( y = -2 \).

Would you like to explore more about transformations or have further questions?

Here are some related questions to consider:

1. How would you write the transformation rule using \( r \) notation for a reflection over the line \( x = 3 \)?
2. Can you express a translation of a function using \( r \) notation?
3. What is the effect of reflecting a function over the line \( y = x \)?
4. How can you identify the transformation rule from the graph of two functions?
5. What are the different types of transformations you can represent using \( r \) notation?

**Tip:** When working with reflections, always ensure the line of reflection is clearly identified, as it directly affects the notation and transformation rule.

Explore how to express the transformation from f(x) = x - 2 to g(x) = -2 - x using the r notation. Understand reflections in functions and learn to apply them in mathematical transformations. Suitable for advanced high school students.

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