4D Practice

4D Practice Problems

Here are some 4D functions for you to practice graphing. The answers have been graphed using a different color for each f value.

1. f(x,y,z) = (x² + y² + z²)^1/2 a. k. a. f(r,t,p) = r

Click here for a hint.

Click here for the answer to problem 1.

2. f(x,y,z) = -x⁴ + 2x² - y² - 2z.

Click here for a hint.

Click here for the answer to problem 2.

3. f(x,y,z) = -x⁴ + 2x² - y⁴ + 2y² - z⁴ + 2z²

For the answer to problem 3, see The Best Homework Ever on Professor Banchoff's home page.




	4D Practice Problems Here are some 4D functions for you to practice graphing. The answers have been graphed using a different color for each f value. 1. f(x,y,z) = (x² + y² + z²)^1/2 a. k. a. f(r,t,p) = r Click here for a hint. Click here for the answer to problem 1. 2. f(x,y,z) = -x⁴ + 2x² - y² - 2z. Click here for a hint. Click here for the answer to problem 2. 3. f(x,y,z) = -x⁴ + 2x² - y⁴ + 2y² - z⁴ + 2z² For the answer to problem 3, see The Best Homework Ever on Professor Banchoff's home page.