Transformations of functions: Horizontal stretches

What You'll Learn

Identify how multiplying x by a constant compresses graphs horizontally

Apply the counteraction principle to predict horizontal stretches and compressions

Calculate new coordinates by dividing or multiplying x-values by stretch factors

Recognize that horizontal transformations are relative to the y-axis

Locate invariant points that remain unchanged during horizontal stretches

What You'll Practice

Graphing f(2x) by compressing functions horizontally by factor of 1/2

Graphing f(x/3) by stretching functions horizontally by factor of 3

Plotting transformed coordinates from original points using stretch factors

Verifying transformations by comparing widths and distances from y-axis

Why This Matters

Horizontal stretches are essential for understanding function transformations in precalculus and calculus. You'll use this skill to model real-world scenarios like sound waves, signal processing, and periodic functions, where compression and expansion represent changes in frequency and time scales.

Before You Start — Make Sure You Can:

Converting from general to vertex form by completing the square Shortcut: Vertex formula Transformations of functions: Horizontal translations

This Unit Includes

2 Video lessons

Skills

Horizontal Stretch

Function Transformations

Compression

Coordinate Mapping

Counteraction Principle

Invariant Points

Graphing

OH Curriculum Aligned