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 .
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 .