Question

a. find the slant asymptote of the graph of the rational function.
b. follow the seven-step strategy and use the slant asymptote to graph the rational function.

$f(x) = \frac{x^2 + 5x - 6}{x - 6}$

Explanation:

Step1: Polynomial long - division

Divide \(x^{2}+5x - 6\) by \(x - 6\).

$$
LATEXBLOCK0
$$

As \(x\to\pm\infty\), \(\frac{60}{x - 6}\to0\).

Answer:

The slant asymptote is \(y=x + 11\).