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The image contains a question asking which functions among \( f(x), g(x), h(x), k(x) \) have horizontal asymptotes, with the following options to select from:

- \( f(x) = \frac{x^2 + 2x}{x^2} \)
- \( g(x) = \frac{x}{\sqrt{x-1}} \)
- \( h(x) = \frac{x^2 + 3x + 2}{x^2 - 1} \)
- \( k(x) = \frac{x^2 - 4}{x - 2} \)

To determine which functions have horizontal asymptotes, we can analyze their behavior as \( x \to \infty \) and \( x \to -\infty \).

### 1. For \( f(x) = \frac{x^2 + 2x}{x^2} \):
As \( x \to \infty \),
\[
f(x) = \frac{x^2(1 + \frac{2}{x})}{x^2} = 1 + \frac{2}{x}.
\]
Since \( \frac{2}{x} \to 0 \) as \( x \to \infty \), \( f(x) \to 1 \). Therefore, \( f(x) \) has a horizontal asymptote at \( y = 1 \).

### 2. For \( g(x) = \frac{x}{\sqrt{x-1}} \):
As \( x \to \infty \),
\[
g(x) \approx \frac{x}{\sqrt{x}} = \sqrt{x}.
\]
Since \( \sqrt{x} \to \infty \), there is no horizontal asymptote for \( g(x) \).

### 3. For \( h(x) = \frac{x^2 + 3x + 2}{x^2 - 1} \):
As \( x \to \infty \),
\[
h(x) = \frac{x^2(1 + \frac{3}{x} + \frac{2}{x^2})}{x^2(1 - \frac{1}{x^2})} = 1 + \frac{3}{x} + \frac{2}{x^2}.
\]
As \( x \to \infty \), the additional terms \( \frac{3}{x} \) and \( \frac{2}{x^2} \) go to 0, so \( h(x) \to 1 \). Thus, \( h(x) \) has a horizontal asymptote at \( y = 1 \).

### 4. For \( k(x) = \frac{x^2 - 4}{x - 2} \):
This expression simplifies using polynomial division:
\[
k(x) = x + 2 + \frac{0}{x-2}.
\]
As \( x \to \infty \), \( k(x) \to x + 2 \), which means the function grows without bound and does not have a horizontal asymptote.

### Conclusion:
The functions that have horizontal asymptotes are \( f(x) \) and \( h(x) \). Therefore, the correct answer is **Fungsi f dan h**.

Would you like more details on how the asymptotes were calculated?

### Relative questions:
1. How can we determine vertical asymptotes for these functions?
2. Why does \( g(x) \) not have a horizontal asymptote despite having a square root?
3. Can functions have more than one type of asymptote (vertical, horizontal, slant)?
4. What is the general rule for finding horizontal asymptotes for rational functions?
5. How does simplifying expressions help in identifying asymptotes?

### Tip:
For rational functions, if the degrees of the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients.

Fungsi mana sajakah yang memiliki asimtot datar?

Learn how to determine horizontal asymptotes for rational functions, focusing on f(x), g(x), h(x), and k(x). Understand how limits and polynomial division are used to find asymptotes in high school-level math problems.

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