Chapter 2.2, Problem 8GP

Solution

To describe: The end behavior of the graph.

  $f\left(x\right)\to -\infty$ as $x\to \infty$ and $f\left(x\right)\to \infty$ as $x\to -\infty$

Given information:

  

Graph:

Consider the following graph.

  

Let $f\left(x\right)$ be polynomial function of the given graph.

From the given graph, it is clear that

  $f\left(x\right)\to -\infty$ as $x\to \infty$ and

  $f\left(x\right)\to \infty$ as $x\to -\infty$

The leading coefficient of $f\left(x\right)$ is negative and the degree of $f\left(x\right)$ is odd.