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$f\left(x\right)=\{\begin{array}{l}x\text{ â¶Ä‰}if\text{ â¶Ä‰}x<−3\\ 2\text{ â¶Ä‰â€‰â¶Ä‰}if\text{ â¶Ä‰}−3≤x<1\\ −2x+2\text{ â¶Ä‰â€‰â¶Ä‰}if\text{ }xâ‰\yen 1\end{array}$

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

Here, $-3$ does not satisfies the inequality $x<-3$. Therefore, end with an open circle at $x=-3$.

The graph of the equation $f\left(x\right)=2$ is constant function for $-3≤x<1$.

Here, $-3$ satisfies the inequality $-3≤x<1$ but 1 does not. Therefore, start with a closed circle at $x=-3$ and end with an open circle at 1.

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

Here, 1 satisfies the inequality $xâ‰\yen 1$. Therefore, start with a closed circle at $x=1$.

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$\left\{y\right|y≤0   or   y=2\}$.