Chapter 2.2, Problem 39E

Solution

To draw the graph of the given polynomial.

  

Given:

  $f\left(x\right)=-x^4$

Calculation:

Consider,

  $f\left(x\right)=-x^4$

The degree is 4 and the leading coefficient is $-1$ .

Here the degree is even and the leading coefficient is negative.

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

When $x=-2$ ,

  $\begin{array}{c}f\left(2\right)=-{\left(-2\right)}^4\\ =-16\end{array}$

When $x=-1$ ,

  $\begin{array}{c}f\left(1\right)=-{\left(-1\right)}^4\\ =-1\end{array}$

When $x=0$ ,

  $\begin{array}{c}f\left(0\right)=-0^4\\ =0\end{array}$

When $x=1$ ,

  $\begin{array}{c}f\left(1\right)=-1^4\\ =-1\end{array}$

When $x=2$ ,

  $\begin{array}{c}f\left(2\right)=-2^4\\ =-16\end{array}$

So the table of values is,

$x$	$-2$	$-1$	$0$	$1$	$2$
$y$	$-16$	$-1$	$0$	$-1$	$-16$

Now the graph is,