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.