Describe in words the level surfaces of $g(x,y,z) = e^{-\left(x^{2}+\left(y-1\right)^{2}+z^{2}\right)}$. Think what the intersections of these surfaces with the three coordinate planes look like.

(a) In symbolic form, these level surfaces are given by $e^{-\left(x^{2}+\left(y-1\right)^{2}+z^{2}\right)} = c$ where $c$ is a constant. For what values of $c$ are level surfaces defined?
$c \in$
(Give your answer as an interval or list of intervals; for example, if c is less than 1 or greater than or equal to 2, enter (-inf,1),[2,inf).)

(b) Pick a level surface that intersects the $xz$-plane. What is your value of $c$?
$c =$
Write the equation for the intersection, as an expression set equal to a constant:
=

(c) Pick a level surface that intersects the $yz$-plane. What is your value of $c$ (which might be different from that you used in (a)?
$c =$
Write the equation for the intersection, as an expression set equal to a constant:
=

(d) Pick a level surface that intersects the $xy$-plane. What is your value of $c$?
$c =$
Write the equation for the intersection, as an expression set equal to a constant:
=