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Here is the graph of the function \( f(x) = \frac{2 - x}{(x - 1)\sqrt{(x - 2)^2}} \). The graph has vertical asymptotes at \( x = 1 \) (shown in red) and \( x = 2 \) (shown in green), where the function becomes undefined.

Key observations:
- At \( x = 1 \) and \( x = 2 \), the function has vertical asymptotes.
- As \( x \) approaches 1 from both sides, \( f(x) \) tends to infinity or negative infinity.
- Around \( x = 2 \), there is a discontinuity since the denominator involves \( (x - 2) \).

Would you like more details on the behavior of the function near these asymptotes or other properties?

Here are 5 questions related to this function:
1. What happens to the function as \( x \to \infty \)?
2. How does the function behave between the two asymptotes at \( x = 1 \) and \( x = 2 \)?
3. What would the graph look like if the denominator didn't have the square root?
4. How does this function behave for negative values of \( x \)?
5. Can the function have any real roots where \( f(x) = 0 \)?

**Tip:** When analyzing rational functions, always check for vertical and horizontal asymptotes by studying the behavior of the function as \( x \) approaches the critical points.

Solve and draw the graph of the function f(x) = (2 - x) / [(x - 1)√(x - 2)^2].

Explore how to solve and graph the function f(x) = (2 - x) / [(x - 1)√(x - 2)^2]. Learn about vertical asymptotes, the function's behavior around critical points, and more. This problem involves key concepts from calculus and algebra, suitable for high school students in Grades 11-12.

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