Answer
Technology used: desmos online calculator,
$f(x)=\{-4 \leq x \leq 0:-1,\ \ 0 < x \leq 4:x\}$
$f(0)=-1$
Work Step by Step
$f(x)=\left\{\begin{array}{lll}
-1 & if & -4 \leq x \leq 0\\
x & if & 0 < x \leq 4
\end{array}\right.$
We build two tables,
one for $-4\leq x \leq 0$,
we join the endpoints with a line segment,
since 0 belongs to this interval, we draw a solid circle for the point $(0,-1)$
$-4$ is in the interval, solid circle for the point $(-4,-1)$
another for $0 < x \leq 4$
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 $(4,4)$
$x=0$ belongs to the interval $-4 \leq x \leq 0$, so we use the rule for that interval
$f(0)=-1$
The technology formula for piecewise defined function has teh form:
$f(x)=\text{\{$ interval:expression, interval:expression $\}}$
Here:
$f(x)=\{-4 \leq x \leq 0:-1,\ \ 0 < x \leq 4:x\}$
