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.