The reciprocal function is the family of functions
If
and
we obtain the graph
shown below.
The reciprocal graphhas several properties.
-
is not defined at
- has asymptotes at
and
meaning that as
and as
- is symmetric in the lines
and
- 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 example
is obtained fromby translatingright by 2, equivalent to the vector
scaling by 7 in the
direction and translating by
is shown below.
