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The image shows a rational function graph with vertical asymptotes at \( x = -4 \) and \( x = 2 \), and a horizontal asymptote at \( y = -3 \). Based on this graph, we need to complete the statements related to the behavior of the function as \( x \) approaches 2 from the right (\( x \to 2^+ \)).

1. **As \( x \to 2^+ \), \( f(x) \to +\infty \)**: The graph indicates that the function tends to infinity as \( x \) approaches 2 from the right, meaning it shoots upwards near the asymptote at \( x = 2 \).

2. **As \( x \to 2^- \), \( f(x) \to -\infty \)**: From the left side, as \( x \) approaches 2, the function decreases without bound, meaning it heads downwards toward negative infinity.

These behaviors describe how the function approaches its vertical asymptote at \( x = 2 \). The dashed vertical line at \( x = 2 \) indicates that the function cannot cross this point, but the values approach infinity from either side.

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### Related Questions:
1. What is the significance of a vertical asymptote in a rational function?
2. How can you determine the horizontal asymptote of a rational function algebraically?
3. Why does the function approach \( +\infty \) from the right and \( -\infty \) from the left of \( x = 2 \)?
4. What happens to the function as \( x \to -4^+ \) and \( x \to -4^- \)?
5. How does the horizontal asymptote \( y = -3 \) affect the end behavior of the function?

**Tip:** Vertical asymptotes occur where the denominator of a rational function equals zero, and the function's behavior around these points often involves values tending towards \( \infty \) or \( -\infty \).

As x approaches 2 from the right (x → 2^+), what happens to f(x)?

Understand the behavior of the rational function as x approaches 2 from the right. This analysis focuses on vertical asymptotes and the function's tendencies toward infinity, covering key topics in rational functions and graph interpretation. Suitable for Grades 11-12.

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