Graph each function. Identify the domain and range.

$f\left(x\right)=\{\begin{array}{l}-xifx\le 3\\ 2ifx>3\end{array}$

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$f\left(x\right)=\{\begin{array}{l}-xifx\le 3\\ 2ifx>3\end{array}$

The graph of the equation $f\left(x\right)=-x$is linear equation for $x\le 3$.

Here, 3 satisfies the inequality $x\le 3$. Therefore, stop with closed circle at $x=3$.

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

The required table is:

The graph of the equation $f\left(x\right)=2$ is constant function for $x>3$.

Here, 3 does not satisfies the inequality $x>3$. Therefore, start with open circle at $x=3$.

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.

Also, the range is $\left\{y\right|y\ge -3\}$.