Answer
If the degree of the numerator term is one more than that of the denominator term, then the graph of the rational function has a slant asymptote. The slant asymptote is given by the quotient function obtained after the simplification of the rational function.
Work Step by Step
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 $y=q\left( x \right)$.
