The function you provided is:

\[
f(x) = \frac{x + 2}{x - 2}
\]

### Properties of the Function

1. **Domain**: The function is defined for all \( x \) except where the denominator is zero. The denominator is \( x - 2 \), so the function is undefined when \( x = 2 \). Thus, the domain is:
   \[
   x \in (-\infty, 2) \cup (2, \infty)
   \]

2. **Vertical Asymptote**: A vertical asymptote occurs when the denominator is zero and the numerator is not zero. Here, the vertical asymptote is at:
   \[
   x = 2
   \]

3. **Horizontal Asymptote**: To find the horizontal asymptote, we analyze the behavior of \( f(x) \) as \( x \to \infty \) or \( x \to -\infty \). Since the degrees of the numerator and denominator are the same (both are first-degree polynomials), the horizontal asymptote is the ratio of their leading coefficients. The leading coefficients are both 1, so the horizontal asymptote is:
   \[
   y = 1
   \]

4. **Intercepts**:
   - **Y-intercept**: Set \( x = 0 \):
     \[
     f(0) = \frac{0 + 2}{0 - 2} = \frac{2}{-2} = -1
     \]
     So, the y-intercept is at \( (0, -1) \).
   
   - **X-intercept**: Set \( f(x) = 0 \), which requires the numerator to be zero:
     \[
     x + 2 = 0 \implies x = -2
     \]
     So, the x-intercept is at \( (-2, 0) \).

### Summary of Key Features
- **Domain**: \( x \in (-\infty, 2) \cup (2, \infty) \)
- **Vertical Asymptote**: \( x = 2 \)
- **Horizontal Asymptote**: \( y = 1 \)
- **Y-intercept**: \( (0, -1) \)
- **X-intercept**: \( (-2, 0) \)

Would you like to see a graph of this function, or do you have any specific questions about it?

### Related Questions:
1. How do you find slant asymptotes for rational functions?
2. What happens to the function \(f(x)\) as \(x\) approaches the vertical asymptote from both sides?
3. How can we determine the concavity of the function \(f(x) = \frac{x+2}{x-2}\)?
4. What is the significance of intercepts in analyzing the graph of a function?
5. How would the function \(f(x) = \frac{x+2}{x-2}\) change if it were transformed into \(f(x) = \frac{x+2}{x-2} + 3\)?

**Tip**: Always analyze both vertical and horizontal asymptotes when dealing with rational functions to understand their end behavior and potential points of discontinuity.

Explore the properties of the rational function f(x) = (x + 2) / (x - 2), including its domain, vertical and horizontal asymptotes, and intercepts. This detailed explanation is ideal for students in Grades 10-12 and covers key algebraic concepts such as asymptotes and intercepts.

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