Answer
$f(x)=\{-2 < $x$ <= 0: $ x^2$ ,\ \ 0 < $x$ < = 4: 1/x\}$
$f(-1)=1$
.
Work Step by Step
$f(x)=\left\{\begin{array}{lll}
-1 & if & -2 < x \leq 0\\
x & if & 0 < x \leq 4
\end{array}\right.$
We build two tables,
one for $-2 < x \leq 0$,
(part of a parabola $ y=x^{2})$
since $-2$ does not belong to this interval,
we draw an empty circle for the point $(-2,4)$
$0$ is in the interval, solid circle for the point $(0,0)$
another for $0 < x \leq 4$
(part of the hyperbola graph for $ y=1/x)$
$\displaystyle \frac{1}{x}$ is not defined for x=0, it rises without bound when x approaches 0,
$4$ is in the interval, solid circle for the point $(4,\displaystyle \frac{1}{4})$
$x=-1$ belongs to the interval $0 < x \leq 4$, so we use the rule for that interval
$f(-1)=(-1)^{2}=1$
The technology formula for piece wise defined function has the form:
$f(x)=\text{\{$ interval:expression, interval:expression $\}}$
Here,
$f(x)=\{-2 < $x$ <= 0: $ x^2$ ,\ \ 0 < $x$ < = 4: 1/x\}$
