Transformations of functions: Vertical stretches

What You'll Learn

Identify vertical stretches and compressions by analyzing transformations outside f(x)

Apply the counteraction principle: forcing y to multiply causes division of y-coordinates

Calculate new y-coordinates by multiplying or dividing based on the stretch factor

Recognize that vertical transformations are measured relative to the x-axis

Distinguish between coefficients inside versus outside the function notation

What You'll Practice

Graphing functions with vertical stretch factors like 1/2, 4/3, and 3

Plotting transformed points by applying stretch factors to y-coordinates only

Verifying stretched graphs by calculating specific coordinate values

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:

Converting from general to vertex form by completing the square Shortcut: Vertex formula Transformations of functions: Vertical translations

This Unit Includes

2 Video lessons

Skills

Vertical Stretch

Function Transformations

Coordinate Mapping

Graphing

Quadratic Functions

Stretch Factor

Compression

OH Curriculum Aligned