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Step functions

The value of the floor function MATH is the largest integer less than or equal to $x$. The floor function is also known as the greatest integer function. The value of the ceiling function MATH is the smallest integer greater than or equal to $x$. The graphs of $f(x)=$ MATH and $f(x)=$ MATH are

graphics/IE_stepfunction__11.png
MATH
graphics/IE_stepfunction__14.png
$f(x)=$ MATH

The floor and ceiling functions are both step functions.

A related function is the fractional part function MATH. The graph of $f(x)=$ $((x))$ looks like
graphics/IE_stepfunction__18.png


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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.

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