## Precalculus (6th Edition) Blitzer

The graph of a rational function $f\left( x \right)=\frac{p\left( x \right)}{g\left( x \right)}$ (where $p\left( x \right)\text{ and }q\left( x \right)$ are the functions of variable $x$ , and $q\left( x \right)\ne 0$ ) has the slant asymptote when the degree of the function of the numerator is 1 more than the degree of the function of the denominator. It can be determined by doing the division. When the numerator is divided by the denominator, then the quotient function obtained is the equation of the slant asymptote of the rational function. Thus, the rational function, after division, can be written as $f\left( x \right)=q\left( x \right)+\frac{r\left( x \right)}{g\left( x \right)}$ And then the slant asymptote of the function $f\left( x \right)$ is given by $y=q\left( x \right)$.