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Overview
Grade 12 Pre-Calculus Mathematics (40S)
Develop algebraic and graphical reasoning through the study of relations
13. Demonstrate an understanding of horizontal and vertical compressions and stretches on function graphs
13.1 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
MB Curriculum Aligned