Given the function

$f(x)=\{\begin{array}{cc}-x^2,& x<mn>0</mn>\\ x^2,& x0\end{array}$

$($a$)$ Graph the function.

$($b$)$ Is the function piecewise continuous $($PWC$)?$

$($c$)$ Is the function piecewise smooth $($PWS$)?$

$($d$)$ Is the function i$)$ continuous, and ii$)$ smooth at $x=0?$ Justify your answer.