Answer
$-1$
See image:
Work Step by Step
Create two tables, one for each interval.
In each table select several x values from the interval and calculate the function values.
Each pair defines a point on the graph.
Plot the points and join with a smooth curve (two curves, one per interval.)
Technology used: geogebra (free online or standalone).
Technology formula: If(-2 < x <= 0, -x\^{}2, If(0 < x < 4, sqrt( x ) )
$\mathrm{x}=-1$ belongs to the first interval, so we use $\mathrm{f}(\mathrm{x})=-\mathrm{x}^{2}$
$\mathrm{f}(-1)=-(-1)^{2}=-1$
