91Ó°ÊÓ

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$g\left(x\right)=\{\begin{array}{l}−1\text{ â¶Ä‰}if\text{ â¶Ä‰}x≤−2\\ x\text{ â¶Ä‰â€‰â¶Ä‰}if\text{ â¶Ä‰}−2<x<2\\ −x+1\text{ â¶Ä‰â€‰â¶Ä‰}if\text{ }xâ‰\yen 2\end{array}$

The graph of the equation $g\left(x\right)=-1$ is constant function for $x≤-2$.

Here, $-2$ satisfies the inequality $x≤-2$. Therefore, end with a closed circle at $x=-2$.

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

Here, $-2  and  2$ does not satisfies the inequality $-2<x<2$. Therefore, begin and closed with a closed circle at $x=-2   and   x=2$.

The graph of the equation $g\left(x\right)=-x+1$ is linear equation for $xâ‰\yen 2$.

Here, 2 satisfies the inequality $xâ‰\yen 2$. Therefore, start with a closed circle at $x=2$.

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 $\left\{y\right|y<2\}$.