Find the slant asymptote of x squared plus one over x then graph it

The graph above shows the function \( f(x) = \frac{x^2 + 1}{x} \) in blue and its slant asymptote \( y = x \) in red (dashed line). As \( x \) becomes very large (positively or negatively), the function \( f(x) \) approaches the line \( y = x \), which confirms that this is indeed the slant asymptote.

Would you like more details on how to analyze or understand this graph? Here are some related questions that might interest you:

1. What are horizontal and vertical asymptotes, and how do they differ from slant asymptotes?
2. How do you find slant asymptotes for other types of rational functions?
3. What is the significance of the remainder in the division when finding slant asymptotes?
4. How do you determine where a function crosses its slant asymptote, if at all?
5. What happens to the function as \( x \) approaches 0 in this specific case?

**Tip:** When analyzing asymptotes, remember that slant asymptotes occur when the degree of the numerator is exactly one higher than the degree of the denominator.

Learn how to find the slant asymptote of the function f(x) = (x^2 + 1) / x using detailed graph analysis. Understand the concept of slant asymptotes and their significance in rational functions. Suitable for high school students in Grades 10-12.

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