Reciprocal of a Function
The following guidelines are useful in order to sketch the reciprocal of a function given the graph of the original function:
Where
is positive or negative then
is also positive or negative respectively.
Where
has zero(s) then the reciprocal function
has vertical asymptote(s) and vice versa.
Where
has a horizontal asymptote at y=c then the reciprocal function
has also horizontal asymptote at
.
Where the original function
is increasing then the reciprocal function
is decreasing.
Where the original function
is decreasing then the reciprocal function
is increasing.
If the original function
has a maximum at
then the reciprocal function
has a minimum at
.
If the original function
has a minimum at
then the reciprocal function
has a maximum at
.
If the original function
has a point of inflexion at
then the reciprocal function
has also a point of inflexion at
.
ways
ways
ways
ways.
