For the function $f(x,y)=e^{-(8x^{2}8y^2)},$ answer the following questions.

a$.$ Find the function's domain.

b$.$ Find the function's range.

c$.$ Describe the function's level curves.

d$.$ Find the boundary of the function's domain.

$4.$ Delemine if the domain is an open region, a closed region, or reather:

f$.$ Declde If the domain is bounded or unbounded.

$($a$)$ Find the function's domain. Select the serrect choice below and, if necestang, fit in the anwer box to complete your choice.

A$.$ The downain is all points except the fistrete poirt $(0,0)$

D$.$ The domain is the entire xyplane.

C$.$ The domain is all points in the flost euadrast.

D$.$ The domain is all points $x,y$ witslying $e^{-(e_r^2{e}_r^2)}>1.$

$($b$)$ Find the function's renge.

The rarge of the function fixy$)$ is $$

$($Type your answer in interval notation$)$