# Increasing Function

## Topic

Functions and Relations

## Definition

An increasing function is a function where the value of the function increases as the input increases.

## Description

Increasing functions are important in mathematics because they describe scenarios where an increase in one variable leads to an increase in another. This is mathematically represented as f(x1​) < f(x2) for any x1 < x2. Increasing functions are used in various fields such as economics to model growth and in natural sciences to describe phenomena like population growth. For example, the function f(x) = 2x + 1 is increasing because as x increases, f(x) also increases. Understanding increasing functions is essential for analyzing trends and making predictions in real-world situations.

For a complete collection of terms related to functions and relations click on this link: Functions and Relations Collection

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