Can you find the horizontal asymptote of f(x)=x+2x−2*f*(*x*)=*x*−2*x*+2​?

To find the horizontal asymptote of the function \( f(x) = \frac{x+2}{x-2} \), we analyze the behavior of the function as \( x \) approaches infinity or negative infinity.

### Steps to find the horizontal asymptote:

1. **Compare the degrees of the numerator and denominator:**
   - The degree of the numerator \( x + 2 \) is 1 (since the highest power of \( x \) is \( x^1 \)).
   - The degree of the denominator \( x - 2 \) is also 1.

2. **Determine the horizontal asymptote:**
   - When the degrees of the numerator and denominator are equal, the horizontal asymptote is found by dividing the leading coefficients of the numerator and denominator.
   - The leading coefficient of the numerator \( x + 2 \) is 1.
   - The leading coefficient of the denominator \( x - 2 \) is 1.

   Therefore, the horizontal asymptote is:
   \[
   y = \frac{1}{1} = 1
   \]

### Conclusion:
The horizontal asymptote of \( f(x) = \frac{x+2}{x-2} \) is:
\[
\boxed{y = 1}
\]

Would you like more details or have any questions?

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**Related Questions:**

1. How do you find the vertical asymptote of \( f(x) = \frac{x+2}{x-2} \)?
2. What is the domain and range of \( f(x) = \frac{x+2}{x-2} \)?
3. Can you find the slant (oblique) asymptote of a rational function?
4. How do you graph the function \( f(x) = \frac{x+2}{x-2} \)?
5. What is the behavior of \( f(x) \) as \( x \) approaches \( 2 \)?

**Tip:** When finding the horizontal asymptote, focus on the highest degree terms in the numerator and denominator, as these dominate the function's behavior for large values of \( x \).

Discover how to find the horizontal asymptote of the rational function f(x) = (x+2)/(x-2). Learn step-by-step analysis of degrees of numerator and denominator, determining horizontal asymptotes by comparing leading coefficients, and conclude that the horizontal asymptote is y = 1. Suitable for advanced high school students and college-level learners.

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