Answer
The graph is shown below:
Work Step by Step
Curve ${{C}_{1}}$ shows the values of the function $f\left( x \right)$ and the curve ${{C}_{2}}$ shows the values of the function $g\left( x \right)$.
The domain of a function can be defined as the set of all values of x for which the function is defined.
Thus the domain of the function $f-g$ is $\left[ -4,3 \right]$.
At $x=-4$:
The value of $f-g$ is:
$\begin{align}
& \left( f-g \right)\left( -4 \right)=f\left( -4 \right)-g\left( -4 \right) \\
& =5-0 \\
& =5
\end{align}$
At $x=-3$:
The value of $f-g$ is:
$\begin{align}
& \left( f-g \right)\left( -3 \right)=f\left( -3 \right)-g\left( -3 \right) \\
& =4-1 \\
& =3
\end{align}$
At $x=-2$:
The value of $f-g$ is:
$\begin{align}
& \left( f-g \right)\left( -2 \right)=f\left( -2 \right)-g\left( -2 \right) \\
& =3-2 \\
& =1
\end{align}$
At $x=-1$:
The value of $f-g$ is:
$\begin{align}
& \left( f-g \right)\left( -1 \right)=f\left( -1 \right)-g\left( -1 \right) \\
& =3-2 \\
& =1
\end{align}$
At $x=0$:
The value of $f-g$ is:
$\begin{align}
& \left( f-g \right)\left( 0 \right)=f\left( 0 \right)-g\left( 0 \right) \\
& =2-1 \\
& =1
\end{align}$
At $x=1$:
The value of $f-g$ is:
$\begin{align}
& \left( f-g \right)\left( 1 \right)=f\left( 1 \right)-g\left( 1 \right) \\
& =1-1 \\
& =0
\end{align}$
At $x=2$:
The value of $f-g$ is:
$\begin{align}
& \left( f-g \right)\left( 2 \right)=f\left( 2 \right)-g\left( 2 \right) \\
& =-1-1 \\
& =-2
\end{align}$
At $x=3$:
The value of $f-g$ is:
$\begin{align}
& \left( f-g \right)\left( 3 \right)=f\left( 3 \right)-g\left( 3 \right) \\
& =-3-0 \\
& =-3
\end{align}$
