Given $f(x)=\{\begin{array}{ccc}1-x^2& if& -32\end{array}$

$($a$)$ Sketch the graph of $f(x).$

$($b$)$ Find $f(2)$

$($c$)$ Find the domain of $f(x).$

$($d$)$ Find the range of $f(x).$

$($e$)$ Find the interval where $f(x)$ is increasing.