Cross Sections of Graphs of Functions of Two Variables

f(x,y)

2

x

-

2

y

direction

x=c

y=c

c

0

The graph of a function of two variables

f(x,y)

can be better understood by looking at slices, or cross sections, of the graph parallel to the

xz

or

yz

planes. Slicing is equivalent to holding

x

(or

y

) constant at

c

and looking at the graph of the resulting single-variable function

f(c,y)

(or

f(x,c)

, respectively). This Demonstration helps students connect the slice on the 3D graph of

f(x,y)

with the 2D graph of

f(x,c)

or

f(c,y)

in its own right.

Joshua Sabloff, Stephen Wang