# Constant Function

## Topic

Functions and Relations

## Definition

A constant function is a function that always returns the same value, no matter the input.

## Description

The constant function is one of the simplest types of functions in mathematics, expressed as

f(x) = c

where c is a constant. This function is significant because it represents scenarios where a quantity remains unchanged regardless of other variables. In real-world applications, constant functions can model fixed costs in economics or steady states in physics. For example, if a company has a fixed production cost of \$500, regardless of the number of units produced, this can be represented by a constant function. Understanding constant functions is essential for grasping more complex functions and for modeling real-world situations where certain variables remain unchanged.

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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         • Relations and Functions 2021 definition, function, relations, glossary terms