# Composition and Transformations

Composition and Transformations

One way to visualize composition is to decompose into and and plot the graph of each in its respective coordinate planes. You can then follow the arrows: Plug into to get ; then plug into to get ; and finally match up and to get a point on . The inside function depends on a parameter , which may be changed. Equivalently, this construction is the projection onto the - plane of the intersection of the surfaces and .

z=f(g(x))

z=f(y)

y=g(x)

x

g(x)

y

y

f(y)

z

x

z

z=f(g(x))

g(x)

a

x

z

z=f(y)

y=g(x)