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) = (x^{2} + y^{2} + z^{2})^{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) = x^{4} + 2x^{2}  y^{2}  2z. Click here for a hint. Click here for the answer to problem 2. 3. f(x,y,z) = x^{4} + 2x^{2}  y^{4} + 2y^{2}  z^{4} + 2z^{2} For the answer to problem 3, see The Best Homework Ever on Professor Banchoff's home page.
