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 function $f+g$ 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
$\begin{align}
& \left( f+g \right)\left( -3 \right)=f\left( -3 \right)+g\left( -3 \right) \\
& =4+1 \\
& =5
\end{align}$
At $x=-2$:
The value of $f+g$ is
$\begin{align}
& \left( f+g \right)\left( -2 \right)=f\left( -2 \right)+g\left( -2 \right) \\
& =3+2 \\
& =5
\end{align}$
At $x=-1$:
The value of $f+g$ is
$\begin{align}
& \left( f+g \right)\left( -1 \right)=f\left( -1 \right)+g\left( -1 \right) \\
& =3+2 \\
& =5
\end{align}$
At $x=0$:
The value of $f+g$ is
$\begin{align}
& \left( f+g \right)\left( 0 \right)=f\left( 0 \right)+g\left( 0 \right) \\
& =2+1 \\
& =3
\end{align}$
At $x=1$:
The value of $f+g$ is
$\begin{align}
& \left( f+g \right)\left( 1 \right)=f\left( 1 \right)+g\left( 1 \right) \\
& =1+1 \\
& =2
\end{align}$
At $x=2$:
The value of $f+g$ is
$\begin{align}
& \left( f+g \right)\left( 2 \right)=f\left( 2 \right)+g\left( 2 \right) \\
& =-1+1 \\
& =0
\end{align}$
At $x=3$:
The value of $f+g$ is
$\begin{align}
& \left( f+g \right)\left( 3 \right)=f\left( 3 \right)+g\left( 3 \right) \\
& =-3+0 \\
& =-3
\end{align}$
