$f(x, y) = 2x - 3y + 1$ Table MV.TMD1 |
3D $f(x, y) = 2x - 3y + 1$ GraphMV.TMD1 |
$f(x, y) = 2x - 3y + 1$ Mapping Diagram
MV.TMD1 |

The same function is visualized in 3D Graph MV.TMD1.

Mapping Diagram MV.TMD1 visualizes only the data that $f(1,0)=3$.

In **Graph TMD1**, the graph of the table values of the
function $f$, we identify each pair of numbers, row $a$ and column $b$, with the entry $f(a,b)$ from
the table with the point in the plane in 3 dimensional space with coordinates $(a,b, f(a))$.

I**n Diagram ****TMD1**, the mapping diagram of the table
values of the function $f$, we identify points on the source
lines (on the left) with a numbers in the $y$ row, $a$ and $x$
column $b$ on the table. We identify a point on the target line (on the
right) with
value of the function $f$ applied to those numbers, $f(a,b)$ also
found in the table in row $a$, column $b$.. An arrow is drawn from
the points on the source lines, $a$ and $b$, to the
corresponding point on
the target line, $f(a,b)$, that visualizes the relation between
the
corresponding numbers in the table.

For example, consider in **Table TMD1**, row $0$ and
column $1$ with entry $3$. In **Graph** **TMD1** these three numbers corresponds to the
point in the graph with coordinates $(1,0,3)$. In mapping **Diagram
TMD1 **this triple corresponds to the point $1$ on the $x$ source
line and $0$ on the $y$ source line of the diagram, the point $3$ on the $z$ target line the diagram
and the arrow from the points representing $1$ and $0$ to $3$ indicating
the function relating the three numbers.

A mapping diagram visualizes a corresponding function table. The
numbers of the table are represented by points on the three lines in the figure. The function relation that the table
displays implicitly by having corresponding numbers in the same
row and column is visualized in the mapping diagram by the arrows. While
the relative size of the numbers in the target column of the table
is not represented in the display, the mapping diagram uses the
number line order to represent this aspect of the function's
values.