The equation provided is:

\[
Y = \frac{10}{|2 - x|}
\]

### Key Characteristics:

1. **Domain**: The absolute value function \(|2 - x|\) ensures that the denominator is always non-negative. However, for the function to be defined, the denominator cannot be zero. So, we solve:
   \[
   |2 - x| \neq 0 \implies x \neq 2
   \]
   Therefore, the domain of \( Y \) is all real numbers except \( x = 2 \).

2. **Behavior**:
   - As \( x \) approaches 2 from the left or right, \(|2 - x|\) approaches 0, making \( Y \) tend towards infinity. Hence, there is a **vertical asymptote** at \( x = 2 \).
   - For large positive or negative values of \( x \), \(|2 - x|\) grows large, and thus \( Y \) approaches 0.

3. **Range**: Since \(|2 - x|\) is always positive (but never 0), \( Y \) is always positive as well. The range of \( Y \) is \( Y > 0 \).

Would you like me to plot the graph or provide further details?

### Related Questions:
1. What is the effect of shifting \( x \) in the absolute value function?
2. How do we find horizontal asymptotes for rational functions?
3. What happens to the graph of \( Y \) if we change 10 to another constant?
4. What is the difference between using absolute value and without it in rational functions?
5. Can you explain how to compute the limits of this function at specific points?

**Tip**: The vertical asymptote occurs where the denominator of a rational function tends to zero. This typically signals a point of discontinuity.

Explore the rational function Y = 10/|2 - x|, covering key algebraic concepts such as asymptotes and the behavior of absolute value functions. Learn about the function's domain, range, and vertical asymptote at x = 2, ideal for Grades 10-12.

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