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The question asks you to determine the horizontal or vertical asymptote of the function \( f(x) = \frac{3}{x+4} \).

### 1. Vertical Asymptote:
To find the vertical asymptote, we set the denominator equal to zero:
\[
x + 4 = 0 \quad \Rightarrow \quad x = -4
\]
Thus, the vertical asymptote is at \( x = -4 \), which corresponds to option **d**.

### 2. Horizontal Asymptote:
For the horizontal asymptote, we analyze the behavior of the function as \( x \to \infty \) or \( x \to -\infty \). Since the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is \( y = 0 \), which corresponds to option **b**.

### Answer:
- **Option d**: \( x = -4 \) is the correct vertical asymptote.
- **Option b**: \( y = 0 \) is the correct horizontal asymptote.

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Here are five related questions:
1. How do you find the vertical asymptote of rational functions in general?
2. What happens to the function \( f(x) \) near the vertical asymptote?
3. How do horizontal asymptotes differ from vertical asymptotes in terms of function behavior?
4. Can a function have more than one vertical asymptote?
5. How does the degree of the numerator and denominator influence the horizontal asymptote?

**Tip**: Vertical asymptotes occur where the denominator is zero, while horizontal asymptotes represent the function's end behavior as \( x \to \pm \infty \).

Tentukan asimtot datar grafik fungsi f(x) = 3 / (x + 4)

Learn how to determine the vertical and horizontal asymptotes of the rational function f(x) = 3 / (x + 4). Understand key concepts like vertical and horizontal asymptotes, and how to apply the vertical and horizontal asymptote theorems. Suitable for Grade 10-12 students.

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