Question

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

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

Short answer

Using the graphing utility the asymptotes and holes of the function $R\left(x\right)=\frac{x^3+x^2+3x+3}{x^4+x^3+2x+2}$are verified.

Step-by-step solution

Step 1. Given Information 

We are given a rational function $R\left(x\right)=\frac{x^3+x^2+3x+3}{x^4+x^3+2x+2}$.

We need to use a graphing utility and verify the asymptotes and holes of the function.

Step 2. Graph the function and verify the result 

The graph of the function $R\left(x\right)=\frac{x^3+x^2+3x+3}{x^4+x^3+2x+2}$is given as

It can be seen that the graph is discontinuous at two points. At $x=-\sqrt[3]{2}$there is a vertical asymptote and at $x=-1$there is a hole at $\left(-1,4\right)$.

So the results are verified.