Graph each function. Identify the domain and range.

$g\left(x\right)=\{\begin{array}{l}-1ifx<0\\ -x+2ifx\ge 0\end{array}$

The domain of the function is the set of all input values and range of the function is the set of all output values.

The given function is

$g\left(x\right)=\{\begin{array}{l}-1ifx<0\\ -x+2ifx\ge 0\end{array}$

The graph of the equation $g\left(x\right)=-1$is constant function for $x<0$.

Here, $-1$does not satisfies the inequality $x<0$. Therefore, stop with open circle at $x=-1$.

Put various values of x and obtained the respective y values.

The required table is:

The graph of the equation $g\left(x\right)=-x+2$is linear function for $x\ge 0$.

Here, 0 does satisfies the inequality$x\ge 0$. Therefore, start with closed circle at $x=0$.

The graph of the function is shown below:

Here, it can be observed that the domain of the function is the set of all real values because the function can take any value of x.

The range is $\left\{y\left|y\le 2\right|\right\}$