Overview

Financial and Workplace Mathematics 120

Geometry

4. Demonstrate an understanding of transformations of a 2-D shape or a 3-D object

4.10 Transformations of functions: Horizontal stretches

Horizontal Stretch and Compression of Functions

See how multiplying the input of a function stretches or compresses its graph sideways, with clear rules, graphs, and step-by-step examples.

What You'll Learn

A horizontal stretch replaces x with x divided by b inside a function, spreading the graph away from the y axis when b is greater than 1

A horizontal compression happens when b is between 0 and 1, pulling the graph toward the y axis

Horizontal transformations act in the opposite direction to what the number inside the function seems to suggest

Every point on the original graph maps to a new point by multiplying only its x coordinate by b, leaving y unchanged

A negative stretch factor combines a horizontal stretch or compression with a reflection across the y axis

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

Learning resources

Skills

Horizontal Stretch

Function Transformations

Compression

Coordinate Mapping

Counteraction Principle

Invariant Points

Graphing

NB Curriculum Aligned