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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
A. Exponential and Logarithmic Functions
7. 12AF.A2.3
7.6 Transformations of functions: Vertical stretches
Vertical Stretch and Compression of Functions
See exactly how multiplying a function by a number stretches or compresses its graph vertically, with step-by-step examples.
What You'll Learn
A vertical stretch multiplies every output of a function by a constant a, moving points farther from the x axis.
When a is greater than 1 the graph stretches vertically; when a is between 0 and 1 the graph compresses (shrinks) toward the x axis.
The transformation only changes y-values, so every point (x, y) on the original graph moves to (x, a times y).
A negative value of a combines a vertical stretch or compression with a reflection across the x axis.
Vertical stretches leave the domain of a function unchanged but can change its range.
What You'll Practice
1
Graphing functions with vertical stretch factors like 1/2, 4/3, and 3
2
Plotting transformed points by applying stretch factors to y-coordinates only
3
Verifying stretched graphs by calculating specific coordinate values
4
Comparing heights of original and transformed parabolas
Why This Matters
Vertical stretches are essential for modeling real-world phenomena where quantities scale up or downlike amplifying sound waves, adjusting spring constants in physics, or analyzing exponential growth rates. Mastering this transformation prepares you for advanced functions in precalculus and calculus.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Learning resources
Skills
Vertical Stretch
Function Transformations
Coordinate Mapping
Graphing
Quadratic Functions
Stretch Factor
Compression
ON Curriculum Aligned