The Reciprocal Function
The reciprocal function is the family of functionsIfandwe obtain the graphshown below.
The reciprocal graphhas several properties.
is not defined at
has asymptotes atandmeaning that asand as
is symmetric in the linesand
has rotational symmetry order 2 about the origin.
All other reciprocal functions can be obtained from this simple graph by a combination of translations, reflections, rotations and scalings. For exampleis obtained fromby translatingright by 2, equivalent to the vectorscaling by 7 in thedirection and translating by
is shown below.