Answer
An exponential cylinder.
Work Step by Step
No x in the equation. The trace in the plane $x=0$ (the yz plane) will be translated along the x-axis into planes $x=k$.
In the yz plane, we have the graph of $z=e^{-y}$
z-intercept: (0,0,1), the graph approaches +y but never crosses it.
Translate the curve into planes $x=k$, to obtain an exponential cylinder.
