Identifying Function Type From Interval Data

A function $g$ is defined by $g(x) = f(x+3)$, where $f$ is an unknown function. For $g$, the input intervals $[2, 6]$, $[6, 18]$, and $[18, 54]$ correspond to the equal-length output intervals $[1, 2]$, $[2, 3]$, and $[3, 4]$, respectively. What type of function must $f$ be?