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The image you've uploaded shows a graph of a rational function with behavior indicating a vertical asymptote at \( x = 3 \). As the function approaches \( x = 3 \) from both sides, the graph heads towards infinity, which is characteristic of a vertical asymptote. There is no indication of the function value approaching a specific number, which would suggest the presence of a hole. Therefore, the correct statement is:

"There is a vertical asymptote at \( x = 3 \)."

Do you need further details or have any other questions about this topic? Here are some related questions you might consider:

1. What happens to the graph of a rational function at a vertical asymptote?
2. How can you distinguish between a hole and a vertical asymptote on a graph?
3. What causes a rational function to have a vertical asymptote?
4. Could there be any horizontal asymptotes in this graph? How can you tell?
5. How does the degree of the numerator and denominator affect the graph of a rational function?

**Tip**: To explore the behavior of a rational function around its asymptotes or holes, consider factoring its numerator and denominator to identify common factors and their impact on the function's graph.

The graph of a rational function f(x) is given. Which of the following statements is true?
1. There is a hole at x = 3.
2. There is a vertical asymptote at x = 3.
3. There is a hole at x = -3.
4. There is a vertical asymptote at x = -3.

Analyze the behavior of rational functions to determine vertical asymptotes. This example demonstrates how the graph of a rational function indicates the presence of a vertical asymptote at x = 3. Explore the key concepts related to asymptotes and how to differentiate between holes and asymptotes in rational functions.

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