Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 176: 44

See the full explanation below.

We plot the graphs of 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: $\begin{align} & x=-2 \\ & f\left( x \right)={{x}^{2}} \\ & ={{\left( -2 \right)}^{2}} \\ & =4 \end{align}$ $\begin{align} & x=-1 \\ & f\left( x \right)={{x}^{2}} \\ & ={{\left( -1 \right)}^{2}} \\ & =1 \end{align}$ $\begin{align} & x=0 \\ & f\left( x \right)={{x}^{2}} \\ & ={{\left( 0 \right)}^{2}} \\ & =0 \end{align}$ $\begin{align} & x=1 \\ & f\left( x \right)={{x}^{2}} \\ & ={{\left( 1 \right)}^{2}} \\ & =1 \end{align}$ $\begin{align} & x=2 \\ & f\left( x \right)={{x}^{2}} \\ & ={{\left( 2 \right)}^{2}} \\ & =4 \end{align}$ The coordinates of $g\left( x \right)={{x}^{2}}-2$ for $x=-2$ to $x=2$ are as follows: $\begin{align} & x=-2 \\ & g\left( x \right)={{x}^{2}}-2 \\ & ={{\left( -2 \right)}^{2}}-2 \\ & =2 \end{align}$ $\begin{align} & x=-1 \\ & g\left( x \right)={{x}^{2}}-2 \\ & ={{\left( -1 \right)}^{2}}-2 \\ & =-1 \end{align}$ $\begin{align} & x=0 \\ & g\left( x \right)={{x}^{2}}-2 \\ & ={{\left( 0 \right)}^{2}}-2 \\ & =-2 \end{align}$ $\begin{align} & x=1 \\ & g\left( x \right)={{x}^{2}}-2 \\ & ={{\left( 1 \right)}^{2}}-2 \\ & =-1 \end{align}$ $\begin{align} & x=2 \\ & g\left( x \right)={{x}^{2}}-2 \\ & ={{\left( 2 \right)}^{2}}-2 \\ & =2 \end{align}$