Chapter 2.2, Problem 10GP

Solution

To graph: The function $f\left(x\right)=-x^3+x^2+x-1$

Graph is as follows.

  

Given information:

Function is $f\left(x\right)=-x^3+x^2+x-1$ .

Graph:

Consider the polynomial function $f\left(x\right)=-x^3+x^2+x-1$ .

To graph the function, make a table of values and plot the corresponding points.

Connect the points with smooth curve and check the end behavior.

The table is as follows:

  $\begin{array}{cccccc}x& -2& -1& 0& 1& 2\\ y& 9& 0& -1& 0& -3\end{array}$

The graph of the polynomial function is as follows:

  

The degree is odd and leading coefficient is negative.

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