Name: _____________________________________
Extra Section 9.1 Practice - OPTIONAL
Draw a sketch of and describe each of the following three-dimensional figures.
1. x 2 + y2 = 9
2. y2 + z 2 = 1
3. z = y 2
4. xy = 1
5. x 2 + y2 = z
6. Picture a plane in R3. This plane divides space into how many regions?
7. How many regions can be formed by two planes?
8. What is the maximum number of regions that can be formed by three planes?
9. What are the other possible numbers of regions that can be so formed?
10. What is the maximum number of regions that can be formed by four planes?
11. Using graphing technology, draw the surface x + 2y + z = 1.
12. Now draw some other surfaces of the form Ax + By + Cz = 1. What do they have in common?
13. There is a great variety of surfaces of the form Ax 2 + By2 + Cz 2 = 1. By plugging in different
values of A, B, and C, see how many you can find. Don’t forget to try negative and zero values of
these parameters!