Chapter 8.4, Problem 35PPS

To determine

To graph the given function.

Explanation of Solution

Given information:

The function is given as,

  $f\left(x\right)=\frac{2x^4+10x^3+12x^2}{x^2+5x+6}$

Graph:

Notice that,

  $\frac{2x^4+10x^3+12x^2}{x^2+5x+6}=\frac{2x^2\cancel{\left(x+2\right)}\cancel{\left(x+3\right)}}{\cancel{\left(x+2\right)}\cancel{\left(x+3\right)}}=2x^2$

Therefore, the graph of $f\left(x\right)=\frac{2x^4+10x^3+12x^2}{x^2+5x+6}$ is the graph of $f\left(x\right)=2x^2$ ,

with a hole at $x=-2\text{ and }x=-3$

  

Interpretation:

The graph of the given function is obtained with a hole at $x=-2\text{ and }x=-3$ .