Chapter 2.6, Problem 25PPS

To determine

Graph each function. Identify the domain and range.

Answer to Problem 25PPS

Domain is all real numbers.

Range $\left\{g\left(x\right)|g\left(x\right)\ge 0\right\}$.

Explanation of Solution

Given information:

Graph each function. Identify the domain and range.

  $g\left(x\right)=\left|x+2\right|$

Calculation:

Parent function of absolute value function,

  $f\left(x\right)=\left|x\right|$

Is defined as,

  $f\left(x\right)\{\begin{array}{l}x\\ 0\\ -x\end{array}$ $\begin{array}{l}if,x>0\\ if,x=0\\ if,x<0\end{array}$

Now consider the given function,

  $g\left(x\right)=\left|x+2\right|$

Defined as,

  $g\left(x\right)\{\begin{array}{l}x+2\\ 0\\ -\left(x+2\right)\end{array}$ $\begin{array}{l}if,x>-2\\ if,x=-2\\ if,x<-2\end{array}$

Create a table of values,

  $\begin{array}{cccccc}x& -3& -4& -2& 1& 2\\ g\left(x\right)& 1& 2& 0& 3& 4\end{array}$

Use maple to graph the function,

  

Hence the domain is all real numbers and range is $\left\{g\left(x\right)|g\left(x\right)\ge 0\right\}$ .