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Algebra II
6. CC.HSF.IF.B.4
6.5 Combining transformations of functions
Combining Transformations of Functions
Apply multiple transformations, like a reflection and two shifts, together to one function.
What You'll Learn
Multiple transformations, like reflections and shifts, can apply together.
In g(x) = a f(x-h) + k, a controls reflection/stretch, h and k shift the graph.
A negative sign reflects the graph over the x-axis.
h shifts horizontally opposite its sign; k shifts vertically by its sign.
Track the vertex or a few key points to see the combined effect.
What You'll Practice
1
Graphing functions with five or more combined transformations step-by-step
2
Converting function notation into horizontal and vertical transformation components
3
Mapping coordinates from parent functions to transformed functions using formulas
4
Identifying and transforming key points (endpoints and turning points)
Why This Matters
Combining transformations is essential for understanding how complex functions behave in precalculus and calculus. This skill allows you to quickly visualize and graph sophisticated functions without plotting dozens of points, saving time on tests and preparing you for advanced function analysis.
This Unit Includes
5 Video lessons
Practice exercises
Learning resources
Skills
Function Transformations
Horizontal Translation
Vertical Translation
Reflections
Stretches and Compressions
Coordinate Mapping
Graph Sketching
OH Curriculum Aligned