Suppose $f$ is a real valued function with domain a subset of  real numbers, $D$.

Definition: $f$
is a linear fractional function if there a numbers $a,b,c$, and $d$ so that for any $x \in D$,  $f(x) =\frac {ax+b}{cx +d}$
Comment: An important result about linear fractional functions shows the relation of these functions to the core negative power function $R(x)=\frac 1 x$.
Theorem LFF.COMP.