Find the slant asymptote and select the graph of the function \( f(x)=\frac{x^{2}+4}{x} \)

To find the slant asymptote, start by rewriting the function:   f(x) = (x² + 4)⁄x Divide each term in the numerator by x:   f(x) = x + 4/x The term 4/x goes to 0 as x becomes very large or very negative. Therefore, the function behaves like:   f(x) ≈ x  as x → ±∞ This means that the slant (oblique) asymptote is:   y = x Additional properties of the graph include: • A vertical asymptote at x = 0 (since the function is undefined there). • Two branches: one for x > 0 and one for x < 0. • For large |x|, the graph approaches the line y = x. The graph of f(x) = x + 4/x will have a dashed line showing the slant asymptote y = x, and the branches will approach this line as x moves away from 0. The branch in the first quadrant (x > 0) and in the third quadrant (x < 0) reflect this behavior.