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Mathematics Essentials 12
Ratio, Rate, and Proportion
15. Sketch enlargements and reductions of objects using various scales
15.1 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
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
Learning resources
Skills
Horizontal Stretch
Function Transformations
Compression
Coordinate Mapping
Counteraction Principle
Invariant Points
Graphing
NS Curriculum Aligned