The Reciprocal Function
The reciprocal function is the family of functionsIf
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 exampleis obtained from
by translating
right by 2, equivalent to the vector
scaling by 7 in the
direction and translating by
is shown below.