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
Where
Where
Where the original function
Where the original function
If the original function
If the original function
If the original function
