Answer
a. see image
b. see image
c. see image
Work Step by Step
a.
In the xy plane ($\mathbb{R}^{2}$), $y=e^{x}$ and contains points $(x,e^{x})$. Thus, the graph is an exponential function (see image).
b.
We can say for case (a), that the points contained are $(x,e^{x},0)$
In $\mathbb{R}^{3}$ the points contained are $(x,e^{x},z)$, where z can be any value.
The surface is obtained by translating the graph from the xy-plane along the z-axis (see image).
c.
This surface contains points $(x,y,e^{y})$, where x can be any value. It is obtained by translating the graph of the exponential function $z=e^{y}$ (which is in the plane where x=0), along the x-axis (see image).
