Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 176: 40

See the full explanation below.

We plot the graphs of the functions $f\left( x \right)=x$ and $g\left( x \right)=x-4$ with the help of the points individually for $f\left( x \right)$ and $g\left( x \right)$. We find the coordinates of $f\left( x \right)$ for $x=-2$ to $x=2$ as follows: $\begin{align} & x=-2 \\ & f\left( x \right)=x \\ & =-2 \end{align}$ $\begin{align} & x=-1 \\ & f\left( x \right)=x \\ & =-1 \end{align}$ $\begin{align} & x=0 \\ & f\left( x \right)=x \\ & =0 \end{align}$ $\begin{align} & x=1 \\ & f\left( x \right)=x \\ & =1 \end{align}$ $\begin{align} & x=2 \\ & f\left( x \right)=x \\ & =2 \end{align}$ The coordinates of $g\left( x \right)$ for $x=-2$ to $x=2$ are as follows: $\begin{align} & x=-2 \\ & g\left( x \right)=x-4 \\ & =-2-4 \\ & =-6 \end{align}$ $\begin{align} & x=-1 \\ & g\left( x \right)=x-4 \\ & =-1-4 \\ & =-5 \end{align}$ $\begin{align} & x=0 \\ & g\left( x \right)=x-4 \\ & =0-4 \\ & =-4 \end{align}$ $\begin{align} & x=1 \\ & g\left( x \right)=x-4 \\ & =1-4 \\ & =-3 \end{align}$ $\begin{align} & x=2 \\ & g\left( x \right)=x-4 \\ & =2-4 \\ & =-2 \end{align}$