The function \( f(x) = |x - 2| + |2 - x| \) can be simplified.

Note that:

\[
|x - 2| = |2 - x|
\]

This is because the absolute value function ignores the sign of its argument, and \( x - 2 \) and \( 2 - x \) are negatives of each other. Therefore:

\[
f(x) = |x - 2| + |2 - x| = 2|x - 2|
\]

Thus, the redefined function is:

\[
f(x) = 2|x - 2|
\]

This is the simplified form of the function.

Would you like a detailed explanation on how to further analyze or graph this function? 

Here are 5 related questions you might find helpful:
1. What is the behavior of the function \( f(x) = 2|x - 2| \) as \( x \) approaches 2?
2. How do you graph \( f(x) = 2|x - 2| \)?
3. How does the function change if we modify the constant inside the absolute value?
4. Can this function be represented piecewise?
5. How does this function compare to \( f(x) = |x| \)?

**Tip:** Absolute value functions create "V-shaped" graphs, symmetric around the point where the argument inside the absolute value equals zero.

Redefine the function f(x) = |x - 2| + |2 - x|.

Learn how to simplify the absolute value function f(x) = |x - 2| + |2 - x| by recognizing key properties of absolute values. This solution focuses on algebraic manipulation and provides a clear breakdown for students in Grades 9-12.

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