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The image shows two graphs of the rational function \( f(x) = \frac{-3}{x - 2} \), along with prompts to identify and draw the horizontal and vertical asymptotes.

### For the **horizontal asymptote**:
A rational function of the form \( f(x) = \frac{a}{x - h} \), where \( a \) is a constant, typically has a horizontal asymptote determined by the degree of the numerator and denominator.

In this case, since the degree of the numerator (constant: -3) is less than the degree of the denominator (linear: \( x - 2 \)), the horizontal asymptote is:
\[
y = 0
\]

### For the **vertical asymptote**:
The vertical asymptote occurs where the denominator equals zero, which is when:
\[
x - 2 = 0 \quad \Rightarrow \quad x = 2
\]
Thus, the vertical asymptote is:
\[
x = 2
\]

### Final answers:
- **Horizontal asymptote**: \( y = 0 \)
- **Vertical asymptote**: \( x = 2 \)

Would you like further details on how these asymptotes are determined? Here are 5 related questions:

1. What happens to the graph of a rational function near its vertical asymptote?
2. How does the degree of the numerator and denominator affect the horizontal asymptote?
3. Can a rational function have multiple vertical or horizontal asymptotes?
4. How can you identify oblique asymptotes in rational functions?
5. How do transformations affect the position of asymptotes?

**Tip**: When identifying horizontal asymptotes, always check the degrees of the numerator and denominator to see if one exists and where it lies.

Graph the horizontal and vertical asymptotes for the rational function f(x) = -3 / (x - 2) and write their equations.

Learn how to graph and identify the horizontal and vertical asymptotes of the rational function f(x) = -3 / (x - 2). Understand the key concepts, formulas, and step-by-step methods to find asymptotes, suitable for students in Grades 9-12.

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