Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 176: 39

See the full explanation below.

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: $\begin{align} & x=-2 \\ & f\left( x \right)=x \\ & =-2 \end{align}$ $\begin{align} & x=-1 \\ & f\left( x \right)=x \\ & =-1 \end{align}$ $\begin{align} & x=0 \\ & f\left( x \right)=x \\ & =0 \end{align}$ $\begin{align} & x=1 \\ & f\left( x \right)=x \\ & =1 \end{align}$ $\begin{align} & x=2 \\ & f\left( x \right)=x \\ & =2 \end{align}$ Now, the coordinates of $g\left( x \right)$ for $x=-2$ to $x=2$ are as follows: $\begin{align} & x=-2 \\ & g\left( x \right)=x+3 \\ & =-2+3 \\ & =1 \end{align}$ $\begin{align} & x=-1 \\ & g\left( x \right)=x+3 \\ & =-1+3 \\ & =2 \end{align}$ $\begin{align} & x=0 \\ & g\left( x \right)=x+3 \\ & =0+3 \\ & =3 \end{align}$ $\begin{align} & x=1 \\ & g\left( x \right)=x+3 \\ & =1+3 \\ & =4 \end{align}$ $\begin{align} & x=2 \\ & g\left( x \right)=x+3 \\ & =2+3 \\ & =5 \end{align}$