Question

For Problems 83 – 88, use a graphing utility to graph the functions R given in Problems 77– 82. Verify the solutions found above.

$R\left(x\right)=\frac{x^3-3x^2+4x-12}{x^4-3x^3+x-3}$

Short answer

By using a graphing utility the asymptotes and hole of the function are verified.

The graph of the function is

Step-by-step solution

Step 1. Given Information

The given rational function is $R\left(x\right)=\frac{x^3-3x^2+4x-12}{x^4-3x^3+x-3}.$

We have to use the graphing utility to graph the function and verify the solutions of asymptotes and holes of the function.

Step 2. Sketch the graph and verify the solutions

The graph we get by using the graphing utility is

From the graph, we can depict that the graph has two discontinuities one at $x=-1,$there is a vertical asymptote and the second when $x=3,$there is a hole at $\left(3,\frac{13}{28}\right).$

Thus, the solutions are verified.