Here is the graph of the function \( f(x) = x + \frac{1}{x+3} \). The red dashed line indicates a vertical asymptote at \( x = -3 \), where the function is undefined.

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Here are some related questions:
1. How do you find the asymptotes of a rational function?
2. What are the intercepts of the function \( f(x) = x + \frac{1}{x+3} \)?
3. How does the function behave near the asymptote at \( x = -3 \)?
4. What happens to the function as \( x \) approaches infinity?
5. How do transformations affect the graph of a function?

**Tip:** Always consider the domain of the function when sketching its graph, as certain values may cause the function to be undefined.

Explore the graph of the function f(x) = x + 1/(x + 3), including its vertical asymptote at x = -3. Learn about rational functions, asymptotes, and behavior near critical points. Suitable for advanced high school students and beyond.

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