Example 5:  $m = 1; b = 1  f (x) = x + 1$

Unlike the previous examples, in this case it is not a single point that determines the mapping figure, but the single arrow from $0$ to $1$, which we  designate as $F[1,1]$.
It can also be shown that this single arrow completely determines the function.Thus, given a point / number,  $x$, on the source line, there is a unique arrow passing through $x$ parallel to $F[1,1]$ meeting the target line a unique point / number, $x + 1$, which corresponds to the linear function's value for the point/number, $x$.
The single arrow completely determines the function  $f$.
Given a point / number,  $x$, on the source line,
there is a unique arrow through $x$ parallel to $F[1,1]$
meeting the target line at a unique point / number, $x + 1$,
which corresponds to the linear function's value for the point/number, $x$.