CALCULUS Understanding Its Concepts and Methods

Step functions

The value of the floor function
is the largest integer less than or equal to
.
The floor function is also known as the greatest
integer* *function. The value of the
ceiling function
is the smallest integer greater than or equal to
.
The graphs of
and
are

The floor and ceiling functions are both step functions.

A related function is the *fractional part *function
.
The graph of
looks
like

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.