# Translating a Function

## Topic

Functions and Relations

## Definition

Translating a function involves shifting the graph of the function horizontally, vertically, or both, without changing its shape.

## Description

Translating functions is significant in mathematics because it helps in understanding how functions behave under shifts. A function can be translated horizontally by adding or subtracting a constant to the input, and vertically by adding or subtracting a constant to the output. For example, translating the function

f(x) = x2

horizontally by 2 units results in

f(x−2) = (x − 2)2

Translations are used in various fields, including physics for wave transformations and in engineering for signal processing. Understanding translations is essential for analyzing and manipulating functions in mathematical modeling and real-world applications.

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