Each arrow passes through a single point, which is labeled $F = [1/2,1]$.

The point $F$ completely determines the function $f$.

Given a point / number, $x$, on the source line,

there is a unique arrow passing through $F$

meeting the target line at a unique point / number, $ \frac 1 2x + 1$, which corresponds to the linear function's value for the point/number, $x$.