Question

find the oblique asymptote and sketch the graph of the rational function.
f(x) = (x^2 + 4)/x
find the oblique asymptote.
y =
(simplify your answer.)

Explanation:

Step1: Perform polynomial long - division

Divide $x^{2}+4$ by $x$. Using the rule of polynomial long - division $\frac{x^{2}+4}{x}=\frac{x^{2}}{x}+\frac{4}{x}=x+\frac{4}{x}$.

Step2: Analyze the behavior as $x\to\pm\infty$

As $x\to\pm\infty$, the term $\frac{4}{x}\to0$. The oblique asymptote is the linear part of the result of the long - division.

Answer:

$y = x$