Answer
Technology used: desmos online calculator,
$f(x)=\{-4\leq x<0:x,\ \ 0\leq x\leq 0:2\}$
$f(0)=2$
.
Work Step by Step
$f(x)=\left\{\begin{array}{lll}
x & if & -4\leq x<0\\
2 & if & 0\leq x\leq 4
\end{array}\right.$
We build two tables,
one for $-4\leq x<0$,
we join the endpoints with a line segment,
since 0 does not belong to this interval, we draw an empty circle for the point (0,0)
$-4$ is in the interval, solid circle for the point (-4,-4)
another for $0\leq x\leq 4$
we join the endpoints with a line segment,
since both 0 and 4 belong to this interval,
we draw a solid circles around the endpoints (0,2) and (4,2)
$x=0$ belongs to the interval $0\leq x\leq 4$, so we use the rule for that interval
$f(0)=2$
For the technology used (desmos.com online calc)
The technology formula for piecewise defined function has teh form:
$f(x)=\text{\{$ interval:expression, interval:expression $\}}$
Here:
$f(x)=\{-4\leq x<0:x,\ \ 0\leq x\leq 0:2\}$
