In Problems $7-44$, follow Steps $1$through $7$on page $228$to analyze the graph of each function.

$R\left(x\right)=\frac{6}{x^2-x-6}$

$R\left(x\right)=\frac{6}{x^2-x-6}$

which may also written as,

$R\left(x\right)=\frac{6}{\left(x+2\right)\left(x-3\right)}$

The domain of$R$is,$\left\{x|x\ne -2,3\right\}$

The $x$- intercept can be determined by finding the real zeros of the numerator of $R$which is in the lowest terms.

Therefore, by solving we have no real zeros.

Hence, there is no $x$- intercept. The $y$- intercept can be found by determining the value of $R$when $x=0$and the value for $R$is $-1$when $x=0$. Hence, the $y$- intercept is,$-1$.

So, the vertical asymptotes are, $x=\left\{-2,3\right\}$.

There is no horizontal asymptote of the graph. So, let us calculate the oblique asymptotes. This can be found by dividing the numerator by denominator and the part except the remainder is the asymptote.

In $R$when we do this procedure, we can find,

$y=\frac{2x+4}{x-1}$

Therefore, the polynomial has neither horizontal nor oblique asymptote.