The problem is asking to find the slant asymptote of the function:

$f(x) = \frac{x^2 + 1}{x + 2} = x - 2 + \frac{5}{x + 2}$

To determine the slant asymptote, we focus on the quotient obtained through long division, which is $x - 2$. The remainder $\frac{5}{x + 2}$ approaches zero as $x$ approaches infinity, so it does not affect the asymptote.

Thus, the slant asymptote is:

$y = x - 2$

Would you like more details or have any questions?

5 Relative Questions:

1. How do you perform polynomial long division to find the slant asymptote?
2. What is the significance of the remainder term in the long division for asymptotes?
3. How do horizontal asymptotes differ from slant asymptotes in rational functions?
4. What happens to the remainder term as $x$ approaches infinity in such divisions?
5. Can a function have both a horizontal and a slant asymptote?

Tip:

To find slant asymptotes, you only need to divide the numerator by the denominator using long division and ignore the remainder as $x$ approaches infinity.