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The question asks: "Over what interval is the graph of \( y = |x - 2| \) increasing?"

To solve this:

The function \( y = |x - 2| \) is an absolute value function, with a vertex at \( x = 2 \). The graph of \( y = |x - 2| \) is a V-shape, with the lowest point at \( x = 2 \).

- To the left of \( x = 2 \) (i.e., for \( x < 2 \)), the function is decreasing.
- To the right of \( x = 2 \) (i.e., for \( x > 2 \)), the function is increasing.

So, the graph of \( y = |x - 2| \) is increasing for \( x > 2 \).

**Answer:** The graph is increasing over the interval \( (2, \infty) \).

Would you like further details or explanations? Here are some related questions:

1. What does it mean for a function to be increasing or decreasing?
2. How do you find the vertex of an absolute value function?
3. What are the general properties of the function \( y = |x - a| \)?
4. How can you determine if a function is increasing using calculus?
5. How do transformations affect the graph of an absolute value function?

**Tip:** To quickly recognize intervals of increase or decrease, observe the slope or derivative of the function!

Over what interval is the graph of y = |x - 2| increasing?

Explore the interval of increase for the absolute value function y = |x - 2|. This detailed solution covers graphing, identifying the vertex, and understanding the behavior of the function across different intervals.

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