https://file.aiquickdraw.com/mathbot/file/1728960573868ixtw66w3.jpg

To interpret the graph and complete the given statement "As \( x \to 0^+ \), \( f(x) \to \) ?", let's analyze the behavior of the rational function near \( x = 0 \) from the right-hand side (which is indicated by \( x \to 0^+ \)).

From the graph:
- As \( x \) approaches \( 0 \) from the positive side (\( 0^+ \)), the function appears to shoot upward sharply.
- This suggests that \( f(x) \) tends toward \( +\infty \).

Therefore, the completed statement is:

\[
\text{As } x \to 0^+, f(x) \to +\infty.
\]

Would you like a detailed explanation of the graph's behavior or any further questions?

Here are 5 questions to further your understanding:
1. What is the difference between approaching from the right (\( x \to 0^+ \)) and from the left (\( x \to 0^- \))?
2. Can you identify vertical or horizontal asymptotes from this graph?
3. What happens to \( f(x) \) as \( x \) approaches negative values close to 0 (\( x \to 0^- \))?
4. How can you determine the type of rational function based on its asymptotic behavior?
5. What does the end behavior of this graph suggest about the degree of the numerator and denominator in the rational function?

**Tip:** When analyzing graphs, vertical asymptotes occur where the denominator of the rational function is zero, provided the numerator is non-zero at those points.

This math problem helps analyze the behavior of a rational function as x approaches 0 from the positive side. The graph shows asymptotic behavior, leading to f(x) → +∞. Suitable for Grades 11-12 studying limits and rational functions.

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