Question

1. which type of asymptote will the following polynomial have: *

$r(x)=\frac{x^{2}-x - 2}{x - 6}$

a horizontal asymptote

b slant asymptote

Explanation:

Step1: Divide the polynomials

Use polynomial long - division. Divide \(x^{2}-x - 2\) by \(x - 6\).

$$
LATEXBLOCK0
$$

Step2: Analyze the asymptote

As \(x\to\pm\infty\), \(\frac{28}{x - 6}\to0\). The function \(r(x)\) approaches the line \(y=x + 5\) (a non - horizontal, non - vertical line).

Answer:

B. Slant Asymptote