Solve, a. Find the slant asymptote of the graph of the rational function f(x) =(x3 - 1)/(x2 - 9). b. Follow the seven-step strategy and use the slant asymptote to graph the rational function.

Consider the provided rational function,

$f\left(x\right)=\frac{\left(x^3-1\right)}{\left(x^2-9\right)}$

Find the slant asymptote of the graph of the rational function.

First we check the our function has slant asymptote.

So, we can check by given rational function.

If the numerator has a power that is larger than that of the denominator then the function has slant asymptote.

Then we apply the long division method.

And we do not need to finish the long division problem to find the remainder.

We only need the terms the equation of the line.