Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 176: 45

See the full explanation below.

We have to plot the graphs of the functions with the help of the points individually for $f\left( x \right)$ and $g\left( x \right)$. The coordinates of $f\left( x \right)$ for $x=-2$ to $x=2$ are as follows: $\begin{align} & x=-2 \\ & f\left( x \right)=\left| x \right| \\ & =\left| -2 \right| \\ & =2 \end{align}$ $\begin{align} & x=-1 \\ & f\left( x \right)=\left| x \right| \\ & =\left| -1 \right| \\ & =1 \end{align}$ $\begin{align} & x=0 \\ & f\left( x \right)=\left| x \right| \\ & =\left| 0 \right| \\ & =0 \end{align}$ $\begin{align} & x=1 \\ & f\left( x \right)=\left| x \right| \\ & =\left| 1 \right| \\ & =1 \end{align}$ $\begin{align} & x=2 \\ & f\left( x \right)=\left| x \right| \\ & =\left| 2 \right| \\ & =2 \end{align}$ The coordinates of $g\left( x \right)=\left| x \right|-2$ for $x=-2$ to $x=2$ are as follows: $\begin{align} & x=-2 \\ & g\left( x \right)=\left| x \right|-2 \\ & =\left| -2 \right|-2 \\ & =0 \end{align}$ $\begin{align} & x=-1 \\ & g\left( x \right)=\left| x \right|-2 \\ & =\left| -1 \right|-2 \\ & =-1 \end{align}$ $\begin{align} & x=0 \\ & g\left( x \right)=\left| x \right|-2 \\ & =\left| 0 \right|-2 \\ & =-2 \end{align}$ $\begin{align} & x=1 \\ & g\left( x \right)=\left| x \right|-2 \\ & =\left| 1 \right|-2 \\ & =-1 \end{align}$ $\begin{align} & x=2 \\ & g\left( x \right)=\left| x \right|-2 \\ & =\left| 2 \right|-2 \\ & =0 \end{align}$