The Reciprocal Function

The reciprocal function is the family of functionsIfandwe obtain the graphshown below.

The reciprocal graphhas several properties.

  1. is not defined at

  2. has asymptotes atandmeaning that asand as

  3. is symmetric in the linesand

  4. 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.