## Sketching Graphs of 1 over f

Given a functionto sketch the graph ofnote the following:

ifasthenfrom above asand ifasthenfrom below as

iffrom above asthenasand if from below asthenas

ifhas a maximum atthenhas a minimum atand ifhas a minimum atthenhas a maximum at

Ifhas a minimum atthenhas a maximum atand ifhas a minimum atthenhas a maximum at

Example:equals 0 when approaching 0 alternately from above and below.

whenand -1 whenWhenthis is a maximum forso a minimum forand whenthis is a minimum forso a maximum for

The graphs ofandare sketched below.