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Algebra I
28. CC.HSF.BF.B.3
28.3 Transformations of functions: Vertical translations
Transformations of Functions: Vertical Translations
Discover how adding or subtracting a constant outside a function slides its whole graph straight up or down without changing its shape.
What You'll Learn
A vertical translation moves every point of a graph the same distance up or down, keeping its shape unchanged.
The rule g(x) equals f(x) plus k shifts the graph up when k is positive and down when k is negative.
Vertical translations change the range of a function but never change its domain.
Any point (x, y) on f(x) becomes (x, y plus k) on the translated graph g(x).
Vertical translations are one of several transformations, alongside horizontal translations and reflections, that reshape or reposition a graph.
What You'll Practice
1
Graphing functions after vertical shifts up and down
2
Rewriting equations to identify vertical translation direction
3
Plotting transformed points by adding or subtracting from y-coordinates
4
Verifying shifts by substituting values into translated equations
Why This Matters
Vertical translations are essential for understanding how functions transform in algebra and calculus. You'll use this skill to graph families of functions, model real-world situations where baseline values shift, and build toward more complex transformations in advanced math courses.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Learning resources
Skills
Function Transformations
Vertical Translations
Graphing
Coordinate Plane
y-axis Shifts
Quadratic Functions
OH Curriculum Aligned