Let 
and 
be two functions. The composite function 
is defined by: for 
. The value 
can be found from the graphs of 
and 
as follows.
Explanation of the figure. For a default value
(shown by the red square), the red line parallel to the 
-axis meets the graph of 
at 
. The green line moves from the point
, parallel to 
-axis, to meet the line 
and gives us the point 
. From there, the dark orange line moves parallel to the
-axis to meet the graph of the function 
at point 
, and from there the dark-blue line moves parallel to the 
-axis, from the position 
to 
, resulting in the value 
given by the blue box. 
Instructions for using the Applet.
- Select one function for
from the combo box. - Select another function for
from the combo box. The insert box may be used. - Move the red square to a new
-value on the axis to see 
.