# Distorting a Function Horizontally

## Topic

Functions and Relations

## Definition

Distorting a function horizontally involves stretching or compressing the graph of the function along the x-axis.

## Description

Horizontal distortions of functions are significant because they alter the input values while maintaining the overall shape of the graph. This is mathematically represented as

f(kx)

where k is a constant. If k > 1, the function compresses horizontally, and if 0 < 𝑘 < 1, it stretches.

Horizontal distortions are used in various fields, including physics for wave transformations and in engineering for signal processing. For example, the function f(2x) compresses the graph of f(x) by a factor of 2. Understanding horizontal distortions 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