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 .