Chapter 3.5B, Problem 14GCE

To determine

To graph:The piecewise function .

Explanation of Solution

Given: $f\left(x\right)=\{\begin{array}{cc}-2x& \text{if }x<0\\ -x^4+2x^3+3x^2+3x& \text{if }x\ge 0\end{array}$

The graph give function is,

  $f\left(x\right)=-2x$ for all value of x less than 0.

  $f\left(x\right)=-x^4+2x^3+3x^2+3x$ for all value of x greater than equal to 0

  

To determine

To graph: The piecewise function $g\left(x\right)$ .

Explanation of Solution

Given: $g\left(x\right)=\{\begin{array}{ccc}{\left(x+4\right)}^3-2& & \text{if}x<-2\\ x^2+2& & \text{if }-2\le x\le 2\\ -{\left(x-4\right)}^3-2& & \text{if }x>2\end{array}$

The graph give function is,

  $g\left(x\right)={\left(x+4\right)}^3-2$ for all value of x less than -2.

  $g\left(x\right)=x^2+2$ for all value of x greater than equal to -2 and less than equal to 2.

  $g\left(x\right)=-{\left(x+4\right)}^3-2$ for all value of x greater than 2.