Chapter 6.8
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
1
Graphing f(2x) by compressing functions horizontally by factor of 1/2
2
Graphing f(x/3) by stretching functions horizontally by factor of 3
3
Plotting transformed coordinates from original points using stretch factors
4
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:
This Unit Includes
2 Video lessons
Skills
Horizontal Stretch
Function Transformations
Compression
Coordinate Mapping
Counteraction Principle
Invariant Points
Graphing
OH Curriculum Aligned
