# Even Function

## Topic

Functions and Relations

## Definition

An even function is a function that satisfies the condition f(x) = f(−x) for all x in its domain.

## Description

Even functions are important in mathematics because they exhibit symmetry about the y-axis. This property is useful in various fields, including physics and engineering, where symmetry simplifies analysis and problem-solving. For example, the function

f(x)=x2

is even because f(x) = f(−x). Even functions are used to model phenomena that are symmetric, such as the distribution of forces in a balanced system. Understanding even functions helps in recognizing patterns and simplifying calculations in mathematical and real-world contexts.

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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