Connections between Multi-Variable Mapping Diagrams and Graphs.
In the left frame are sliders for three variables:  $x_P, y_P, z_P$ and we will consider a mapping diagram and the corresponding point $P = (x_P,y_P,z_P)$ in 3 dimensional cartesian geometry in the right frame.

Initially in the right frame is a mapping diagram  with arrows, $<x_P,y_P>$, between the point $x_P=3$ on the first axis, $X$ the point $y_P=1$ on the second axis, $Y$; $<y_P,z_P>$, between the point $y_P=1$ on the second axis, $Y$ and the point $z_P=3$ on the third axis, $Z$; and $<x_P,z_P>$, between the point $x_P=3$ on the first axis,$X$ and  the point $z_P=3$ on the third axis, $Z$. You can move the sliders freely with your mouse and see the corresponding mapping diagram changes in the right frame.
 
To remove the arrows and the mapping diagram that corresponds to the point P: Uncheck the box in the left frame  "Show Parallel Axes" .
Removing the check in  the box will hide the arrow and points in the mapping diagram in the right frame.

To see the point  $P=(x_P,y_P,z_P)$ in a cartesian coordinate 3- space that corresponds to the mapping diagram: Check the box in the left frame  "Show Point in 3 Space [use axes toggle]" and  toggle the coordinate axes in the 3D frame on the right.
In the 3D coordinate- frame space will appear the point with coordinates $(x_P,y_P,z_P) = (3,2,3)$ and coordinate axes.
You can move the sliders freely in  left frame with your mouse and see the corresponding point move.in the 3D coordinate frame.
Removing the check in this box will hide the point in the coordinate space..

To return to the mapping diagram, reverse the processes.