Chapter 2.2, Problem 6P

Solution

To find: The interval for x , and $y=f\left(x\right)$ that describe a good viewing window for the graph of a polynomial function $f\left(x\right)$ .

The required intervals are $-2<x<4$ and $-38<y<6$.

Given data: The polynomial function is $f\left(x\right)=2x^4-7x^3+x-8$

Method/Formula used:

A good viewing window for the graph of a polynomial function $f\left(x\right)$ that clearly show the end behaviour of the function from $-\infty$ to $\infty$ .

Graph: The good viewing window for the graph of the function $f\left(x\right)=2x^4-7x^3+x-8$ is shown in Fig. (1).

  

Interpretation:

The function $f\left(x\right)=2x^4-7x^3+x-8$ behave as:

  $\begin{array}{c}f\left(x\right)\to \infty \text{as}x\to 4\\ f\left(x\right)\to \infty \text{as}x\to -2\end{array}$

And in the interval $-38<f\left(x\right)<6$ function $f\left(x\right)$ shows above behaviour clearly.

Therefore, the intervals for x , and $y=f\left(x\right)$ that describe a good viewing window for the graph of a polynomial function $f\left(x\right)$ are $-2<x<4$ and $-38<y<6$.