Answer
$f(-2)=4$
$f(-1)=1$
$f(0)=1$
$f(1)=2$
$f(2)=3$
Work Step by Step
$f(x)=\begin{cases}x^{2} \mbox {if }x\lt0\\x+1 \mbox {if }x\ge0\end{cases}$
$f(-2),$ $f(-1),$ $f(0),$ $f(1),$ $f(2)$
$f(-2)$
Since $-2\lt0$, substitute $x$ by $-2$ in $x^{2}$ to find $f(-2)$:
$f(-2)=(-2)^{2}=4$
$f(-1)$
Since $-1\lt0$, substitute $x$ by $-1$ in $x^{2}$ to find $f(-1)$:
$f(-1)=(-1)^{2}=1$
$f(0)$
Since $0\ge0$, substitute $x$ by $0$ in $x+1$ to find $f(0)$:
$f(0)=0+1=1$
$f(1)$
Since $1\ge0$, substitute $x$ by $1$ in $x+1$ to find $f(1)$:
$f(1)=1+1=2$
$f(2)$
Since $2\ge0$, substitute $x$ by $2$ in $x+1$ to find $f(2)$:
$f(2)=2+1=3$