For each function, do the following:
• Sketch the cross-sections f (−1, y), f (0, y), f (1, y), f (x, −1), f (x, 0), f (x, 1), and any others you think
might help you understand the graph of the function.
• Sketch a contour plot of f .
1. f (x, y) = xy
2. f (x, y) = x2
3. f (x, y) = x2 + y
p
4. f (x, y) = x2 + y 2
5. f (x, y) = x2 − y 2
The following equations in x, y, and z are not functions. Still, the set of points in 3-space satisfying the
equation will create a surface in 3-space. For equation, describe the surface.
1. x2 + z 2 = 1
2. x = 1
3. x = y