Greg Kelly, Hanford High School, Richland, Washington

The functions that we have studied this year have all been functions of one independent variable: eg:     

x

2  sin In real life, functions often have more than one independent variable: eg: Area of a triangle:

A

 1 2

bh

   1 2

bh

  

x

2 

y

2 

z

2

w



x

2 

y

2 

z

2 

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.

z

    100

x y

2 

z

 z 100    100

x y

2 10 x 10 sketch of graph y 

z

 z 100    100

x y

2 y 10 10 x 10 10 y x sketch of graph level curves Level curves are drawn by holding the z value constant (similar to contour lines on a topographic map.) 

z

 z 100    100

x y

2 Let’s look at the same graph plotted on the TI-89: 10 x 10 sketch of graph y First change the mode to 3D.

Then go to the Y= screen and enter the equation.



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

p