# Step Function

## Topic

Functions and Relations

## Definition

A step function is a function that increases or decreases abruptly at certain points, creating a series of steps.

## Description

Step functions are important in mathematics because they model situations where changes occur in discrete steps rather than continuously. They are written as piecewise functions with constant values over intervals. Step functions are used in various fields, including economics for modeling tax brackets and in engineering for digital signals. For example, the Heaviside step function is used in control theory and signal processing. Understanding step functions is essential for analyzing and modeling scenarios where abrupt changes occur and for applying mathematical concepts to real-world problems.

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Common Core Standards CCSS.MATH.CONTENT.8.F.A.1, CCSS.MATH.CONTENT.8.F.B.5, CCSS.MATH.CONTENT.HSF.IF.A.1, CCSS.MATH.CONTENT.HSF.IF.A.2, CCSS.MATH.CONTENT.HSF.IF.C.7, CCSS.MATH.CONTENT.HSF.BF.A.1, CCSS.MATH.CONTENT.HSF.BF.B.3, CCSS.MATH.CONTENT.HSF.BF.B.4 6 - 9 Algebra     • Functions and Relations         • Special Functions 2021 definition, function, relations, glossary terms, discrete functions