1. Greg Kelly, Hanford High School, Richland, Washington

2. The functions that we have studied this year have all been functions of one independent variable: eg: In real life, functions often have more than one independent variable: eg:

3. Functions with two independent variables can be represented graphically. This is not easy to do by hand, and our calculators do not do a great job either.

4. y x z 10 100 sketch of graph

5. y x z x y 10 100 sketch of graphlevel curves Level curves are drawn by holding the z value constant (similar to contour lines on a topographic map.)

6. y x z 10 100 sketch of graph Let’s look at the same graph plotted on the TI-89: First change the mode to 3D. Then go to the Y= screen and enter the equation.

7. By pressing the arrow keys, you can rotate this graph! 